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GL Ship Vibration 09 | Resonance | Normal Mode
Uploaded by Deniz Yazgaç
by Iwer Asmussen / Wolfgang Menzel / Holger Mumm Germanischer Lloyd Hamburg, 2001
This issue of GL’s “Technology” contains the revision of an article which originally appeared in the German “Handbuch der Werften”, published in 1998 by Schiffahrtsverlag “Hansa” C. Schroedter & Co., Hamburg. The paper presents the “state of the art” of calculation and measurement techniques in the field of ship vibrations. In this respect, emphasis is put on the description of general procedures. Theoretical background is only explained when necessary for the comprehension of physical concepts. Specifically addressed are engineers/ inspectors at shipyards, shipping companies and consulting offices. The goal is to improve communication between specialists performing vibrational investigations and engineers concerned with the design and operation of ships.
Page 1. Introduction 2. Standards for Assessment
2.1 2.2 2.3 Effect of Vibrations on Human Beings Structural Vibrations Engine and Equipment Vibrations
3. Calculation of Natural Vibrations
3.1 3.2 3.3 Global Structures Substructures Local Structures
4. Calculation of Forced Vibrations
4.1 4.2 4.3 4.4 Computation Methods Damping Excitation Forces Evaluation and Assessment
23 24 24 30
5.1 5.2 5.3 5.4 5.5 Sensors Measurement Systems Measurement Procedures Evaluation and Assessment Practical Applications
34 35 35 37 40
6. Conclusions 7. Literature
Despite considerable progress in the theoretical and experimental treatment of ship vibrations, questions about the accuracy of analysis methods for predicting the vibration behaviour as well as for solving vibration problems on completed ships are as topical as ever. The aim of this article is to describe the “state of the art” in computational and measurement techniques. Here, the main emphasis is placed on the description of general approaches. Theoretical backgrounds are explained only if this is necessary for an understanding of physical situations. This paper is, therefore, aimed in particular at engineers and inspectors of shipyards, shipping companies and consulting offices, in the expectation that improved communication will be achieved between vibration specialists and engineers responsible for design and operation of ships. In this context, “ship vibrations” consist exclusively of elastic vibrations of the ship’s hull and/or its parts. These vibrations can impair well-being, efficiency and the health of people on board, can cause damage to the ship and its cargo, and – in especially serious cases – can endanger the safety of the vessel. The paper is structured as follows: after a discussion of questions concerning the building specification and standards for assessment of ship vibrations, analysis methods for calculation of free vibrations are dealt with. Here, various aspects of the determination of natural frequencies for simple components, large subsystems and entire ships are described. After that, aspects of the calculation and assessment of the forced vibration level are dealt with, since in many cases a final evaluation of vibration questions in the design stage cannot be made with adequate certainty solely by comparing natural frequencies with main excitation frequencies. Finally, this is followed by general remarks about the state of the art for experimental investigations and by a description of some vibration problems experienced on completed ships. The measurement procedure for diagnosis and actions taken to solve these problems are described in detail. Here, it must also be pointed out that the subject of ship vibrations certainly cannot be dealt with completely and conclusively. It is our opinion that highly specialised questions – concerning, for example, elastic mounting of engines, sloshing phenomena in tanks or torsional vibrations of shafts – nevertheless lie outside the scope of this article, important as such questions undoubtedly are.
the type of ship. too. In the newbuilding contract. a few important standards that are often used to define limit values are dealt with briefly. Since the periodic excitation forces of the propulsion plant – especially of the propeller – are subject to a certain degree of variation. too. the propulsion plant.s.2.m. the term “crest factor” is no longer necessary and is thus completely cancelled. At the preliminary design stage or during the structural design phase. the so-called “overall frequency weighted r.1. It is now harmonised with the principles of ISO 2631-1 and integrates substantial improvements. the „combined curve” of ISO 2631-2 [4] is used. The new ISO standard was released in December 2000 [3]. This evaluation procedure contradicted the principles stipulated in the revised edition of ISO 2631-1 [2]. The word “habitability” is often used in this connection.1 ISO 6954 Internationally. value”. the shipyard will carry out adequate analyses or will have them performed by an independent consultant. 2. As frequency weighting curve. This fact led to problems in the assessment because the standard did not clearly define how a “mean” peak value (maximum repetitive value) was to be formed from values of differing magnitude determined over the duration of the measurement – constituting the well-known problem with the “crest factor”. and so on. limit values that must not be exceeded during operation of the ship are defined as being part of the specification. is no longer a peak value. Three classifications for different kinds of spaces are combined with recommended vibration limits. see Fig. Amongst other things. Table 1 Overall frequency-weighted r. An important feature of this standard was that. 1. There are essentially three areas which are often included in the building specification to define vibration limits: •	Effect	of	vibrations	on	human	beings •	Structural	vibrations •	Vibrations	of	engines	and	equipment	items In the following. it shoul basically be noted that existing standards are aimed solely at ensuring comfort and well-being. it has become standard practice to regulate vibration aspects for a newbuilding on a contractual basis. Hence. Standards for Assessment In recent years.1 Effect of Vibrations on Human Beings With regard to the effect of vibrations on human beings.s. For this reason. For assessment. 6 . If the recommended limits are not exceeded. a single value over the frequency range from 1 to 80 Hz is formed. now giving additional orientation to contractual partners. the vibration values.m. a revision of ISO 6954 was initiated.5 NOTE The zone between upper and lower values reflects the shipboard vibration environment commonly experienced and accepted. the scope of theoretical investigations regarded as neces-sary in a given case depends on the agreed limit values. The final vibration criterion. peak values of amplitudes had to be considered individually for each excitation frequency. damage to health is unlikely to occur. The shipyard thus bears the responsibility for ensuring that limits agreed on with the shipping company are not exceeded or – if they are – for taking action with the aim of reducing the vibration level to the permissible value. see Table 1. for the purposes of assessment. values from 1 Hz to 80 Hz given as guidelines for the habitability of different areas on a ship [3] Area classification A mm/s2 Values above which adverse comments are probable Values below which adverse comments are not probable B mm/s 4 2 mm/s2 214 107 mm/s 6 3 mm/s2 286 143 C mm/s 8 4 143 71. 2. NOTE: For guidance. are measured with the corresponding variance. the standard ISO 6954 (edition 1984) gained general acceptance for the evaluation of human exposure to vibrations [1]. Classification A can be passenger cabins.
it better reflects the human sensitivity by taking into account the entire spectrum from 1 to 80 Hz.5 3.0 2.2 1.9 2. The Rules do not only comprise limits and assessment procedures for the normal (seagoing) service con-dition. Table 2 Vibration limits.4 1. For illustration. describing the extent of vibration (and noise) measurements for different criteria and operation modes. short exposure time Public spaces. Moreover.8 1.8 1.6 2.2 1. overhangs 1) Harbour operation hcn 5 1 2 3 4 5 1 Thruster operation 1) hcn 2 3 4 5 hcn 2 3 4 0. The respective GL class notation is called “Harmony Class” [5]. The measurements cover a variable but relatively high percentage of the various kinds of spaces and areas of the ship.Classification B crew accommodation areas.6 2. Generally.0 2. it is still up to owner and yard to exactly define the vibration comfort on board “their” vessel.6 - Thrusters operating at not less than 70% full load 7 .6 3. “combined curve” of ISO 2361-2 The class notation requires a detailed documentation of plans and drawings to be submitted by the building yard. recommended to achieve the hcn number desired.2 2. It is focused on noise and vibration criteria on-board passenger vessels in a first step and will be followed by additional criteria for other types of ships. passenger spaces Sea mode Vibration limits 1 Indoor spaces forward of frame B First-class cabins Standard cabins Public spaces.4 2. reflecting both sound insulation and impact sound insu-lation of cabins to adjacent spaces.0 3.2 2.4 3.2 2. The comfort is scaled according to harmony criteria numbers.0 2. are checked and finally approved.4 2. Germanischer Lloyd was the first Classification Society to base the vibration part on the new ISO 6954 standard. and Classification C working areas. Furthermore.1. leading the user through different technical aspects of noise and vibration on-board passenger ships. with initiative from cruise ship owners.6 2. Table 2 displays the vibration limits for passenger spaces.2 2. the new ISO 6954 is clearer and avoids misunderstandings due to deletion of the crest factor.7 3. “acoustic privacy” is introduced as an additional noise criterion.4 1. A separate section is dedicated to the different theoretical analyses (FEM-based.7 2. The main objective is to support the owner/yard when detailing a newbuilding specifi-cation with regard to vibration and noise. hcn 1 to 5. Fig. for instance).4 2. Therefore. Nevertheless.8 3. 2. Classification Societies.4 2.2 3. The measurements of each space investigated are documented in the Survey Report and finally condensed to an hcn number.0 2. began to introduce vibration and noise as voluntary class notations.2 3. but account for thruster operation and harbour mode as well.8 3.1: Frequency weighting curve. that is – as the final result – certified in the class notation. where 1 represents an extraordinary comfort (most ambitious level).0 1. the rise of the cruise market in the last few years led to advanced developments by Classifi-cation Societies in this field.4 2.0 3.8 3. needed particular attention for passenger ships. Hints to potentially critical areas are given. the Rules are detailed.2 Class Notations In terms of comfort on board. long exposure time Outdoor spaces forward of frame B Open deck recreation Open deck recreation. However.9 3.5 4. On this basis the Survey Programs. obviously.0 2. Notations of comfort.
Therefore. that can be used as a guide in assessing the risk of cracks in local structures as a consequence of vibration. derived from a large number of measurements. 2: Assessment diagram for vibration of structures 2.2 Structural Vibrations Even if the limits of human exposure to vibrations are not exceeded in the accommodation area of a ship. [6] and [7]. in the case of resonance or near-resonance. to avoid premature failure or malfunctions of components. were revised and are widely used today. Here. values are quoted which. have been discontinued. Fig. Typical examples are tank structures or other local components in the aftbody of the ship and in the engine room. such as •	•	•	•	•	•	material structural	details	(stress	concentrations)	vibration	mode welding	processes	applied production	methods	employed	and environment	(corrosive	media) the bandwidth for the possibility of occurrence of cracks is large.2. which also cover – among other things – the scope of the abovementioned discontinued standards. considerable dynamic magnification relative to the edge supports is possible. see Fig. These series are now also published in Germany as DIN ISO standards. Fig. as well as ISO 2372. 2373 and 3945. The risk of damage resulting from inadequate fatigue strength is then particularly high. Because of the many factors that influence the fatigue strength. several standards dealing with engine vibrations were replaced. the wellknown standards VDI 2056 and 2063.3 Engine and Equipment Vibrations In past years. This figure shows two limit curves. In this connection. must not be exceeded by engines. equipment items or peripheral devices. 2. 3: Assessment diagram for engine vibrations 8 . The series ISO 7919 and 10816. vibration problems can nevertheless occur in other areas in which these limit values do not apply. Fig. 3 shows the evaluation curves from [8]. Germanischer Lloyd also published corresponding vibration limits in its Rules [8]. The amplitudes are peak values.
all natural frequencies of the system are higher than the highest significant excitation frequency.	low	values	of	L stiffness and mass (low impedance) •	rrangement	of	living	and	working	quarters	in	the	vicinity	of	A the propeller and main engine to optimise stowage space or to achieve the largest possible deck openings of container ships •	igh	propulsion	power	to	achieve	high	service	speed H •	mall	tip	clearance	of	the	propeller	to	increase	efficiency S by having a large propeller diameter •	se	of	fuel-efficient	slow-running	main	engines	U On the other hand. Fig. In many cases.In general. vibration problems occur more frequently. A subcritical or supercritical design can be selected. In questions of ship technology. The following design trends contributed to this: •	ight	weight	construction	and. the consistent application of labour legislation rules and higher demand for living comfort underline the need to minimise the vibration level. a subcritical design must ensure that. However. The criteria for use of curves A‘. 4: Dynamic magnification factor for a single degree-of-freedom system 9 . The overall hull of the ship takes on different natural modes and natural frequencies for different loading conditions. B. a resonance-free design of structures and equipment items is possible for all service conditions. For example. considering a certain safety margin. different filling states change the natural frequency of tank structures. but also on the damping coefficient of the system. B‘ and C are described in [8] and will not be repeated here. limit curve A can be applied to assess vibration levels regarding machinery items. As shown in Fig. 4. The simplest way to avoid vibrations is to prevent resonance conditions. this prerequisite frequently remains unfulfilled. These criteria mainly involve reciprocating engines with peripheral devices connected to them. limit curve B can also be used to assess equipment and components installed in steering gear rooms or bow thruster compartments. 3. as a rough guide. Difficulties often occur in the assessment of components situated on masts.	therefore. This procedure is successful as long as natural frequencies and excitation frequencies can be regarded as being independent of environmental conditions. The dynamic magnification factor depends not only on the safety margin between excitation frequency and natural frequency. Calculation of Natural Vibrations Because low-cost building and operation aspects of a ship increasingly influence the design. it can be assumed that damage to these components can largely be prevented if the vibration levels remain within area A. or there might be variable excitation frequencies for propulsion plants having a variable speed. however. In addition.
Noise-FEM.g. 5: Natural frequency ranges in shipbuilding applications 10 . The transitions between ship motions. ship vibrations and ship acoustics are smooth. “the number of natural frequencies per Hertz”. vibrations of substructures and local vibrations.In Fig. One then has to make do with characteristic energy values averaged over frequency intervals (Statistical Energy Analysis. as described in [9]. in the meantime FE analyses using 3D models of the hull became the standard computational tool. However. As a result. of course. Thanks to advances in computer technology. Fig. the deckhouse and the doublebottom. Typical large substructures. one had to make do with beam models of a more complex type to cover shear and torsional stiffnesses of the ship’s hull. the system response in the higher frequency range is defined by the interaction of more natural modes than at low frequencies. In the field of vibration. However. frequency-selective computation is limited to partial areas of particular interest.1 Global Structures Global vibrations in this context are vibrations of the ship’s entire hull in the frequency range from about 0. The frequency limits indicated are valid for standard designs and for normal ship types. for which coupled horizontal and torsional vibration modes play an important part. for example. 3. From today’s point of view. it is possible to distinguish between three different phenomena: global hull vibrations. For example. In the transition to structure-borne noise..5 to 10 Hz. FEM is used to some extent in this frequency range.e. are coupled in a way that they cannot be considered isolated. the mode density finally becomes so large that a frequency-selective analysis of the structure’s dynamic behaviour requires an unacceptably large effort. they do not offer the necessary degree of accuracy.. e. computation methods for determining global vibrations progressed rapidly during the past two decades. the higher the frequency. such as engine foundations. classical approximation formulas or simple beam models for determining natural bending frequencies of a ship’s hull are in many cases no longer adequate. the vibration phenomena relevant in shipbuilding applications are plotted versus frequency. the greater the modal density. In the past. with the currently available power of computers. such as the aft part of the ship. an FE model intended for reliable computation of natural frequencies and natural modes of an engine foundation up to a frequency of about 200 Hz has about the same number of degrees of freedom as a complete hull model used to compute the natural vibrations up to 20 Hz. In general. too.). For container ships with a high deck-opening ratio. i. Today. etc. 5.
The number of degrees of freedom is 20 to 40 thousand. Three typical models are shown in Fig. yielding 50 to 150 natural vibration modes in the range up to 20 Hz. The division of the model is oriented relative to deck planes and to main longitudinal and transverse structures. it turns out to be sufficient to represent primary structural components with the aid of plane stress elements. since they are generally simulated by truss elements. 6: FE models of various types of ships 11 .1.500	TEU	container ship.	and	a	4.3. namely.	a	smaller	double-hull	tanker. For global vibrations.1 Modelling The replication of a ship’s structure in an FE model is generally the most laborious step of the analysis. a 700 TEU	container	ship. 6. Large web frames are taken into account by plane stress elements as well. Fig. Bending stiffnesses of deck and wall girders are not covered by this type of modelling. For the sake of simplicity minor structural components lying outside the planes of the modelled sections are considered as additional element thicknesses or are ignored altogether.
at least in the form of beam elements. webs of the deck grillages are modelled three-dimensionally in the case of the yacht only. For the other two much larger ships. However. too. As can be seen from the centre-line sections. and a frigate. the global models are mostly used for strength analyses.Fig. 7: FE models of various types of ship In global vibration analyses. 12 . An alternative for taking account of deck grillages in the form of beam elements is to model the webs of girders by means of plane stress elements and flanges by truss elements. Fig. 7 shows three typical FE models of this kind in an overall view and a longitudinal section: a yacht approximately 60 m long. If the bending stiffnesses of deck grillages are also to be included in the global model. Normally. which require a more accurate modelling of the structure in these areas. the representation of transverse and longitudinal girders of decks is necessary. this procedure would have led to unnecessarily large models. it is not necessary to model the middle and the forward part of the ship with the level of detail shown. a 240 m passenger ship. these models possess 40 to 80 thousand degrees of freedom and have 300 to 500 natural frequencies in the range up to 20 Hz.
for instance. As starting vectors the Lanczos method presented in [13] and [14]. no extreme cargo distributions should be selected. The associated set of potential-theory formulas is based on conformal mappings of a circular cross-section. This arrangement of masses is advisable for heavy parts of equipment whose centres of gravity are not automatically evident from the model geometry. To illustrate the situation. auxiliary structures must be provided to introduce masses into the FE model in a realistic manner.In the computation of global vibrations of ships. in many cases. However. Because of the large deckopening ratio. 13 . In each case. natural vibration calculation can be performed.2 Calculation If stiffness and mass matrices are known. the same numerically effective algorithms can be used for solving the eigenvalue problem as those used for problems involving only structural masses. but rather homo-geneous ones typical for the expected ship operation. at least two or three mass distributions have to be considered. Nevertheless. it should be considered to take a further loading condition into ac-count. therefore. on the other hand. for example for container masses. which involves a 2D theory derived for elongated. The following masses must be taken into account: •	•	•	•	•	Ship	structure Outfitting	and	equipment Tank	filling Cargo Hydrodynamic	masses More comprehensive methods to calculate hydrodynamic inertia effects take account of the fact that the acceleration of a point on the wetted shell also causes changes in the hydrodynamic pressure at adjacent points. it must be borne in mind that natural frequencies are highly dependent on the loading condition. numerically effective approximation methods. If nodes are available. To determine hydrodynamic masses. The masses of tank contents are distributed over the nodes of the relevant tank structure. The procedures used are still often based on the method of Lewis [10]. the existing geometric information of the FE model should be used (element masses). In contrast to strength analyses. The water flow in the ship’s longitudinal direction is taken into account by correction factors that depend mainly on the length-to-width ratio. For the eigenvalue solver. are used. which in turn leads to a considerably more effort-intensive calculation of eigenvalues. slim bodies. selects in an automated manner unit load cases that act in every degree of freedom of the system. starting vectors must be specified.0 m upwards. The three types of masses last mentioned are likewise arranged as node masses. Thus. 9. the first torsional vibration mode and the second vertical bending vibration mode are presented together with the computed natural frequencies. A calculation method that takes account of these couplings is described in [11]. the same applies to cargo masses. For this purpose. separate computations must be performed. the natural vibration analysis of a large global model takes several hours on a high-performance workstation. only mode shapes can be calculated for which corresponding starting vectors have been specified. the superimposition of which permits as accurate a representation as possible of expected vibration modes. As a result of the comparatively short deckhouses there is no significant stiffening effect on the ship’s hull. This leads to the computation of all existing natural frequencies in the desired frequency interval. For cargo vessels. and also on the natural mode being considered. Conversion into a practical computation method on the basis of a boundary value formulation is described in [12]. This coupling leads to the introduction of terms on the secondary diagonals of the mass matrix. taking correct account of the centres of gravity. the selection of correction factors should be co-ordinated with the expected frequency range of natural modes. At present.1. Node masses are concentrated at the respective nodal points of the FE model. 3. For the other ship types presented. The Lewis method offers the advantage that the hydrodynamic mass matrix to be used for the eigenvalue solution contains terms on the main diagonal only. such as the Ritz procedure. Because hydrodynamic masses have to be determined prior to the calculation of natural vibrations. the natural torsional frequencies for container ships are low. a distinction is drawn between node masses and element masses. However. Because of the usual higher excitation frequencies their contribution to the vibration level is small. as well as for the “distributable” part of equipment masses. it is possible to accurately determine only the natural frequency of the particular mode used as the basis to select correction factors. Strictly speaking. For the arrangement of structure masses. it can be assumed that the superstructures contribute considerably to hull stiffness. knowledge of these vibration modes is important for validation purposes. some typical fundamental natural vibration modes calculated for the previous FE models are shown in Fig. In FE techniques. 8 and Fig. From a draught variation of about ± 1. Vibration modes of ship hulls lie in the lower frequency range. It must be ensured that these auxiliary structures do not unacceptably stiffen the ship’s hull.
2 Substructures In the transition between global and local vibrations. for example. vibrations of large subsystems. for the sake of simplicity.1 Hz f = 2.4 Hz f = 3. are of interest in practice. as being independent of the vibration behaviour of the structure surrounding them – which is the case with a vibrating radar mast.6 Hz f = 1. i. the supporting conditions. in the analysis of subsystems.f = 1.6 Hz f = 0. Here subsystems are structures or equipment items whose natural vibration characteristics can be regarded.7 Hz Fig. 14 . because it defines the connecting stiffness. 8: Natural torsional and vertical bending modes of various ship types 3. However.3 Hz f = 2.e. too. the surrounding structure must not be ignored.
in a simplified manner. 9: Natural torsional and vertical bending modes of various ship types 3. 10 shows such a model with the calculated fundamental vibration modes. in particular. The longitudinal and transverse vibration modes.2.7 Hz f = 2. Therefore.6 Hz f = 1. 15 . are significantly affected by the vertical stiffness in the supporting area.f = 5. Fig. an appropriate part of the ship’s hull in the region of the deckhouse into the model. A typical example of a substructure is a deckhouse when considered as an isolated system.2 Hz f = 5. an attempt must be made to incorporate.0 Hz Fig.1 Deckhouses The aim of analyses of this type is the avoidance of resonance between fundamental vibration modes and main excitation frequencies.
in particular.FE model f = 9.9 Hz f = 15. in the vicinity of the main sources of excitation.7 Hz for the transverse mode. the foundation is stiffly constructed. The low-frequency vibration is the in-phase vibration. the natural frequency is defined mainly by the shear stiffness of the deck-house.4 Hz because of the large external dimensions of the deckhouse. The supporting structure governs the vibrational behaviour of the funnel as well. whereas these subsystems in the following vibration mode vibrate in the anti-phase mode at 11. This natural frequency is defined mainly by the grillage stiffness of the bridge deck. Vibration of the upper region of the deckhouse occurs at 17.e. 16 . It is not least due to this fact that an isolated consideration of deckhouses is increasingly giving way to complete global vibration analyses.9 Hz. Thus. leading to a natural frequency of 15. These vibrations attain a significant level in many cases. i. deckhouses are additionally often situated far aft.4 Hz f = 11. For the same reason. whether resonance situations may lead to unacceptably high vibrations. Because of the stiff foundation. vertical vibrations of the aft part of a ship lead to longitudinal vibrations in the upper region of the deckhouse. it is also possible to investigate the effect of design changes in the deckhouse foundation on the vibration behaviour. 10: Natural vibrations of a deckhouse In this way. However. on the basis of such models. There are two coupled natural modes for longitudinal vibrations of the deckhouse and funnel. As can be seen from the natural vibration modes presented. This situation can only be investigated in a forced vibration analysis by taking account of stiffness and mass characteristics of the entire hull and by considering excitation forces realistically. for example.The design proves to be advantageous from the point of view of vibration because the basic recommendations had been adopted: •	inimum	possible	height	and	maximum	possible	length	and	M width of the deckhouse •	tiffly	designed	foundations. the first two of these recommendations are often unachievable. Thus.7 Hz f = 17.4 Hz Fig. The natural torsional vibration frequency is found to have a comparatively high value of 21. Global transverse vibration of the deckhouse does not exist in the frequency range considered.	especially	the	arrangement	of S bulkheads or wing bulkheads under the fore and aft bulkheads of the deckhouse (alternatively: support of longitudinal deckhouse walls on longitudinal bulkheads in the ship’s hull) •	Maximising	the	longitudinal	shear	stiffness	of	the	deckhouse by means of continuous longitudinal walls having as few and small cut-outs as possible For container ships.9 Hz f = 21. it is not possible to assess. a risk of strong vibrations exists in many cases. since couplings with hull vibrations cannot be taken into account.9 Hz. since deckhouses are designed to be both short and tall to optimise stowage space.
respectively. Stays should be provided with pre-tensioning devices and should form as small an angle as possible with the horizontal. A mast vibrating in resonance can also act as a secondary source of excitation. it turns out to be adequate to design fundamental vibration modes of the mast construction subcritically relative to twice the propeller frequency or to the ignition frequency. adequate stiffness of the connecting structural members on deck and of the corresponding foundation must be ensured. experience excitation. four design principles can be distinguished: •	imple	masts	whose	cross-sections	make	them	fairly	flexible	S and which are stiffened by means of additional stays •	Welded	tripod	constructions •	treamline-shaped	masts	with	large.2 Hz Longitudinal vibration 16.2 Hz Fig. As with any design aimed to avoid resonance. Natural frequencies of longitudinal and transverse vibrations are 16. Depending on the size and nature of the equipment fixed to a mast. Transverse vibration 17. it is necessary to select – mainly in conjunction with distance from propeller and main engine – the order of excitation up to which there should be no resonances. there is a clear separation from the surrounding structure. This means that a subcritical design with regard to a frequency twice that of the propeller blade frequency was ensured in this case. In the case of both tripod and latticework designs. This usually involves generation of noise. it turns out that the frequency depends not only on the height and the location of the centre of the mass. As a result. This is the only way to ensure that supporting conditions are taken into account realistically.	closed	cross-sections	and	S correspondingly high bending and torsional stiffness •	ore	complex	beam	type	structures. deck coverings and partial walls can. tronic equipment situated on mast platforms. in turn.	which	are	mostly	designed	M as latticework constructions made of tubular or MSH members In the case of stayed masts. Mounting on deck areas supported by bulkheads is the best solution. In general. but also on the stiffness of the foundation at the footing.2 Hz. this requirement can be met only if communication between steel construction and equipment departments is well coordinated at an early stage.3. The FE model should continue at least down to a level one deck below the mounting deck. Permissible vibrations are mostly defined by limit values for elecFig. 11 shows the possible extent of a computation model for a mast situated on a wheelhouse top. These limits are not standardised. and at present they are mostly based on empirical values.2 and 17. it is possible to position the mast on bulkheads of the stair casing or on pillars integrated in accommodation walls.2 Masts In the case of masts.2. Particularly in the case of masts mounted on the wheelhouse top. 11: Natural vibrations of a mast 17 . In many cases.
5 Hz Rigid engine structure ≈ 7.4 – 15.2 Hz H-type f = 14. Since doublebottom designs for slow-running main engines do not differ significantly. rigidly mounted 7-cylinder engine. compared to those of the engine supported realistically in the ship. see [15]. 12 shows natural modes of a slow-running. For slow-running engines resonance situations can be experienced for all three fundamental modes. with typical combinations of number of cylinders and speed. the engine structure must be simulated with greater accuracy – see also [16]. Rigidly supported L-type f = 13. “X” and “L” modes – depend mainly on the doublebottom stiffness.9 – 6. Fig. but they are also determined to a large extent by the stiffness of adjoining structures. which might be in resonance with the ignition frequency.4 Hz Rigid engine structure ≈ 10.3 Engine/Foundation Systems Subsystems described so far refer to typical shipbuilding structures. bands for the probable natural frequencies can be derived for engines having a certain number of cylinders. 13: Computation model for determining the natural transverse bending frequencies of medium-speed engines 18 . must be included in the model. the engine housing. This shows the port half of the engine room area of a RoRo trailer ferry powered by two 7-cylinder.5 Hz Fig. The global stiffness of the engine housing is represented in a simplified form by means of plane stress elements.8 Hz Realistically supported L-type 9.3.0 Hz H-type 5. Corresponding computation models should contain at least the doublebottom structure in the engine room area and the structure up to the next deck. 12: Natural vibrations of slow-running main engines for various boundary conditions Fig. In the case of medium-speed engines this is true only for the H-type vibration mode. The effect of the doublebottom stiffness is more marked for slow-running engines than for medium-speed ones. Furthermore.8 Hz X-type f = 19. In the following. too. the natural vibration of ships’ main engines are described.2. Fundamental natural frequencies of main engine vibrations depend on the distribution of stiffnesses and masses of the engine itself.1– 9. However. A computation model with a typical level of detail of engine and ship structure is presented in Fig. 13. Because the effect of the engine’s frame stiffness is more marked for medium-speed than for slowrunning engines. corresponding natural frequencies are given for an infinitely rigid engine structure supported on a realistic ship foundation. Fundamental vibration modes of housings – called “H”.400 kW main engines driving two propellers. 4.0 Hz X-type 15.
are not very stiff.5 Hz. Detailed investigations should be considered for a shaft line design for which at least one of the following criteria apply: •	oft	structure	in	the	vicinity	of	the	stern	tube	bearing S •	uidance	of	the	shaft	in	a	shaft	bossing.5 Hz f = 22. For this example various natural frequencies were determined. which tapers off in a catamaran-like manner. springs and damping elements. A corresponding computation model includes both the entire shaft line and the crankshaft – see also [17]. independent of the surrounding structure of the ship.	thus	causing	hydrodyG namic masses to act •	rrangement	of	shaft	brackets. supercritical relative to the ignition frequency of 30 Hz. Bending Vibrations For the determination of natural frequencies of shaft bending vibrations. it is often adequate to consider shaft lines isolated. Because the H-moment also leads to vertical vibrations of the doublebottom. therefore. reflecting coupled vibrations of the port and starboard engines. comparatively strong axial force fluctuations can appear at the thrust bearing.2. Consequently.4 Shaft Lines Axial/ Torsional Vibrations As far as axial and torsional vibrations are concerned.5 and 22. In practice. The design was. this will not be dealt with here. there was no need to install an elastic or semi-elastic mounting. With regard to torsional vibrations. 19 .5 Hz Fig. 14 shows three corresponding vibration modes.	which	themselves	can	have	A natural frequencies close to the propeller blade frequency •	stimation	of	clearance	between	shaft	and	bearing	shell	as	well	E as of dynamic bearing loads in a forced vibration analysis 3. thus indicating an adequate safety margin to the ignition fre-quency as well.9 Hz f = 20. Computations of X-type vibration modes of the main engines revealed frequencies in a band between 34 and 38 Hz. i. If the axial/torsional vibration resonates with the thrust fluctuation of the propeller or with a radial force excitation of the main engine. However. the task was to check the risk of resonance between transverse modes of the engines and the ignition frequency.f = 17. these turn out to be relevant only for shaft sys-tems driven by slow-running main engines. hydrodynamic masses act on the ship. Axial vibrations are usually calculated by isolated models consisting of point masses. Large tank-fillings in the vicinity of the main engines are taken into account as well. Depending on coupling conditions of the port and starboard engines. H-type trans-verse vibration modes occur at 17. relevant requirements of the Classification Society have to be accounted for – see [8]. 20. 14: H-type natural vibration modes of two 7-cylinder engines on a RoRo trailer ferry Because the transverse members in the ship’s aftbody.9. Fig. The same applies to the calculation of coupled torsional/axial vibrations. which have to be considered. it is advisable to take account of the structure surrounding the shaft system. These forces are further transmitted into the ship then acting as a secondary source of excitation.e.
Through an increase in the diameter of the propeller shaft. FE models for their calculation must be detailed. 15: Natural vibrations of a shaft system Fr. turned out to be the critical vibration mode. the relevant natural frequency was raised by about 4 Hz. which is also shown. This can be achieved only if freedom from resonance exists for all structural components of the deck. such as rotational stiffnesses at plate field edges and effective mass distributions. where the first and last of these criteria apply. It is also necessary to take account of the propeller’s hydrodynamic mass moments. in many cases. in contrast to their representation in global computations. it is advisable to perform parametric investigations varying the input data within the range of practical relevance. bending stiffnesses of local structures must be con-sidered as realistically as possible. it turned out that the natural frequency of the vessel’s basic aftbody vibration mode was lower than the fundamental natural frequency of the shaft system itself (6.4 Aftbody transverse vibration at 6. In calculation practice. resulting in an adequate safety margin relative to the propeller blade frequency. In most cases it turns out to be up to an order of magnitude smaller than the stiffness of the adjacent structure.8 Hz).6 Hz Fig. As described in [18]. the oil film stiffness depends on the shaft speed and the static loading of the bearings.5 m. the magnitude of which can certainly equal the mass moments of the “dry” propeller. In addition. among other things. the propeller shaft’s vertical bending vi-bration mode. is given in Fig. 2. vibration amplitudes at the centre of a deck grillage of an accommodation deck should not be much larger than at stiffly supported edges. damage occurred in the aft stern tube bearing. also have to be taken into account here. stiffeners and panels (grillages) – see also Fig. The aim of local vibration investigations is usually to limit vibration magnification relative to the global level.8 as opposed to 8. 2.Shaft in aftbody Shaft vertical bending vibration (side view) at 11. Therefore. for example. 16. Distances between bearings are comparatively uniform in the range of 4. It is obvious that shaft vibration modes couple with structural modes. In particular. other important parameters of influence. In spite of parameterised input possibilities and extensive graphic support. The amount of effort needed for the creation of FE models of such structures should not be underestimated.4 Shaft transverse bending vibration at 8. In the case described here. It involves a beam model of the shaft system integrated in a simple 3D model of the surrounding aftbody of a sailing vessel having a length of about 90 m. computation results concerning shaft bending vibrations always involve some degree of variance. since their natural frequencies are comparatively close together.8 Hz An analysis example. experience has shown that this type of analysis can hardly be carried out within the given time schedule.3 Local Structures Because of comparatively high natural frequencies of local ship structures. 20 . In the case concerned.0 Hz Fr.6 Hz). Thus. since its frequency was close to the propeller blade frequency (10. 15. a distinction is drawn between vibrations of plate fields. The oil film stiffness of slide bearings is an important parameter for the calculation. 3. Although propulsion power was comparatively low. Because of uncertainties in estimating the oil film stiffness and hydrodynamic masses.
The basic assumptions are: •	reely	rotatable. However. this “basic stiffness” will ensure a moderate level. lead to considerable overdimensioning of 21 . main engine. results will be in good agreement with those achieved by more complex methods. the assumption of simply supported edges is conservative. plate thicknesses and dimensions of stiffeners and girders are determined in the preliminary design phase in accordance with relevant Classification Rules. however. an attempt is made to achieve a subcritical design of all structural components relative to the main excitation frequencies. considering frame spacing. For tank walls. of course. models of this quality are used only to determine basic vibration modes of deck panel structures. In particular.2 x twice the propeller blade frequency or main engine ignition frequency in the ship’s aftbody. as verified in a large number of local vibration analyses. The following recommendations for minimum natural frequencies of local structures can be stated as a guide: fnatural > 1. The plate field and stiffener lengths that must not be exceeded are specified for the designer. plate thickness and added mass. based on relevant excitation frequencies. In this connection.2 Design Criteria Normally. In a first step. bow thruster) are considered.For walls.3. This assumption can. the profile type is also used. vibration-related aspects often necessitate stronger dimensioning compared to Rule requirements.1 Calculation Methods For practical calculation of natural frequencies of geometrically simple structures. the best cost/ benefit ratio is certainly offered by beam grillage models. webs of girders and stiffeners must be represented with the aid of membrane or shell elements and flanges by means of truss or beam elements. the effective width of the deck plating to be included in the section moment of inertia of beam elements depends on the vibration mode to be determined. Critical lengths of plate fields can be determined in an iterative process. For these problems. engine room and deckhouse area four times the propeller blade frequency for the ship’s shell structure directly above the propeller fnatural > 1. it is recommended to take an effective added mass of 40 kg/m2 into account for decks in living and working spaces. an added mass of 20 kg/m2 should be chosen.3. If higher modes are to be included in the analysis. However. models with greater precision are required to simulate the stiffening effect in a three-dimensional form. to be considered. but rather to ensure a “basic stiffness” throughout the structure.	non-displaceable	supporting	conditions F at edges •	Rectangular	shape •	Regular	arrangement	of	stiffeners •	No	pillars	or	stanchions	within	the	panel	area •	Uniform	distribution	of	added	mass If these preconditions are not fulfilled. Freely rotatable support can normally be assumed for plate fields. Therefore. for example as mentioned in [19] and [20]. Even in the case of resonances of vibration modes with higher excitation orders. this leads to adequate scantlings of local structures from a vibration point of view. hydrodynamic masses of tank fillings have. the concept of “critical lengths” for the design of plate fields and stiffeners turns out to be useful. such as: •	Curvature	of	the	structure •	Residual	stresses	of	welds	or	distortions	–	see	[21]	•	Vibration	behaviour	of	adjacent	structures Taking account of these imponderables.1 x For a subcritical design. it becomes clear that the main aim is often not to predict natural frequencies of local structures with a high degree of accuracy. Assuming freely rotatable edge conditions. the structures must be reproduced in an FE model. As long as assumptions for the derivation of these formulas are valid. For the calculation of maximum stiffener lengths. In particular. for accommodation decks with higher added masses and tank structures on which hydrodynamic masses act. 3. The distribution of effective masses is often impossible to specify accurately. Fig. 16: Structural components in local vibration calculations 3. There are a number of other parameters that influence natural frequencies of local structures. Only structures situated in the vicinity of main excitation sources (propeller. it is most effective to use analytical approximation formulas. since each constraining effect increases the safety margin between natural frequency and excitation frequency.
effective masses. Thus. the desired aim of reducing the equipment numeral and. for example the anchor gear was achieved. 17. However. Such brackets cause a certain clamping effect that.stiffeners and girders connected via brackets to adjacent structures. the tanks were moved one deck level higher compared to the original design. saving money in the purchase of. it is sufficient to design natural frequencies of structural components subcritically up to about 35 Hz. consequently. 3. the simpler and better the solutions are.3. An alternative is the selection of high-webbed girders (600–800 mm). twice that frequency (≈ 10 and 20 Hz) or the ignition frequency of the main engine (U14	Hz). it was no wonder that cracks shown in the sketch occurred after a comparatively short period of operation. engine speed and filling level. excitation frequencies were either the propeller blade frequency. In these cases the design frequency band is consequently small. the shipyard decided to make a break in the deckhouse front and aft bulkhead in the space under the bridge deck. In these areas. leads to an increased stiffness. although this can lead to comparatively soft panel structures if supporting walls are far away. On the other hand. web heights of 250 to 400 mm are aimed at. in turn. Designs aiming at less than the single blade frequency are inadvisable for reasons of lack of stiffness. and to replace the bulkhead by an open beam structure. To compensate for this. specific structural features. Measurements revealed vibration velocities about 30–50 mm/s at the centre of plate fields and 15–30 mm/s at stiffeners.3 Inclusion in the Design Process The earlier the stage at which vibration-related aspects are included in the design. After raising natural frequencies of all local structures to about 24 Hz. in turn. A supercritical design or a “design in frequency windows” should be chosen with regard to higher dominant excitation frequencies.e. when dominant excitation frequencies are known. To keep the equipment numeral low. a larger amount of computation effort is required to ensure that natural frequencies are calculated with the necessary degree of accuracy. This relationship is manifested by the fact that a ship whose local structures have been consistently designed in respect to vibration also gains acoustic advantages. the problem was solved. The equipment numeral of a ship according to applicable Classification Rules depends on the closed wind-drag area of the deckhouse. Because of operational requirements. However. In such cases. on the one hand. Therefore. there is a strong interaction between local vibrations of structures and ship’s acoustics. sufficient margin to route piping and cables through adequately large cut-outs in webs. Depending on measurement location.4 Case Study The importance of freedom from resonance and of a certain degree of stiffness for structural components is demonstrated exemplarily on damaged freshwater tanks of a container ship. In practice. it is advisable to introduce concepts of the stiffening pattern for decks and tank walls in the ship’s aftbody and deckhouse area. for passenger ships the design of local structures with natural frequencies above 20% of twice the propeller blade frequency is generally impossible to realise for weight reasons. If the shipyard has no experience with this matter. Thus. led to a high vibration level on the bridge deck. severe vibrations of the tank structures occurred. i. The stiffening system of the aft tank-bulkhead and the longitudinal wall is sketched in Fig. In the entire frequency range around nominal speed (110–130 r/min). as this space was not needed for living purposes. structures are designed “in the window” between blade frequency and twice that frequency. In most cases. This retrospective measure had evidently not been checked with regard to vibration aspects. etc. The intermeshing with other design questions is another reason for examining the design from a vibration point of view as early as possible. 3. Even at this early stage. which offer 22 .3. Dimensioning principles stated above are fairly easy to put into practice in the case of cargo vessels. however. provided main engines are mounted elastically. More effort has then to be spent on modelling boundary conditions. Any further increase of natural frequencies requires an unjustifiable amount of effort. this design variant also resulted in a reduced shear stiffness which. an external expert should be consulted after completion of the general arrangement plan and after the propulsion plant has been fixed. One typical example is the choice of web heights of deck girders in the accommodation area. Asymmetrical stiffener profiles exhibited vibration velocities of up to 30 mm/s in their flange plan. The close relationship between vibration related questions and other design targets is illustrated by the example of a container ship that exhibited large vibrations on the bridge deck. bracket connections are often accounted for in the design process by taking about 70– 50 % of the actual bracket length as “effective” in the analysis. web heights that can be implemented are limited by restricted deck heights and by the need for adequate space under the flange plane of the deck grillage for routing of piping and cable runs.	A	rough	check	indicated that natural frequencies of all structural components of the tanks lay in the range between 10 and 20 Hz.
Due to this a reduction of the effort needed to solve the equation system is achieved. the mode superposition method. Basically. Ultimately.	it	must	be	proven	during	sea	trials	that	maximum	vibration velocities specified in the newbuilding contract are not exceeded. orthogonal coordinates. but must also give an insight into vibration amplitudes expected at critical points. Because of its extraordinarily high numerical effectiveness. the solution 23 .1 Computation Methods A large number of FE programs provide various algorithms for solving the equation of motion of forced vibrations in MDOF (“Multiple Degree of Freedom”) systems. for example. Therefore. a distinction has to be drawn between solutions in the time domain and those in the frequency domain. In ship structural applications. 4. in the time domain is confined to special cases. the first step is to determine natural vibrations of the structure in the frequency range of interest. achieved great acceptance for calculation of the forced vibration level. In addition to a realistic simulation of stiffness and mass characteristics of the structure. it is thus necessary to consider damping and excitation forces. [22] and [23]. it is possible to compute the vibration level even for large systems over a wide range of frequencies at moderate cost.Fig. can be distinguished by a characteristic frequency content. Vibration questions in shipbuilding mainly involve types of excitation which are either harmonic or which are capable of being represented as a harmonic series and. a complete judgement of ship vibrations cannot be limited to an analysis of the free vibration problem. Natural modes are then transformed and used as generalised. Calculation of Forced Vibrations The greater the mode density. the more difficult it becomes to apply the criterion of resonance avoidance. Computation of forced vibrations often turns out to be the only possibility of assessing on a rational basis the large number of natural frequencies. therefore. Thus. In this process. such as the analysis of the vibration decay of a ship’s hull in the event of excitation by a slamming impact (“whipping”). This procedure causes a decoupling of all degrees of freedom contained in the equation of motion. 17: Vibration damage to a freshwater tank in the aft part of a ship 4.
If the excitation forces do not vary harmonically. can each be thought of as an SDOF (“Single Degree of Freedom”) system.4. it follows that A1/A2 = 1. the logarithmic decrement can be calculated from the modal damping by means of the relation stated above. Thus. with the exception of special problems (e. To illustrate the magnitude of damping. not be definitely identified by measurements. in the case of cardan shafts. Whereas material damping is easy to quantify (0. for container vessels. 18: Modal damping for global calculations of vibrations √1 – ϑ 2 In structural mechanics. satisfactory results for the damping coefficient as a function of frequency were achieved with the approach outlined in Fig. the amplitude decreases by 13% with each vibration cycle.5–1. m = mass √c · m •	Logarithmic	decrement	Λ [-]. a number of different parameters are used: applications. Torsional and axial vibration damping devices of crankshafts as well as hydraulic units of transverse engine stays are examples of mechanical damping systems. Cargo damping is heavily dependent on the nature of the cargo (container.5%). periodically varying excitation forces are of interest. component damping depends mainly on floor and deck coverings (4–10%).3 Excitation Forces In ship technology. For a modal damping of 2%. In the literature. in the case of MDOF systems. It refers to individual natural vibration modes which. the value of Λ is 0. Lehr’s damping coefficient is normally used in the form of modal damping. •	Damping	coefficient	b	=	damping force vibration velocity N   m/s  •	Degree	of	damping	ϑ or Lehr’s damping coefficient D [-]. for example. where Λ = 2·π⋅ϑ Fig.2 Damping Various physical mechanisms contribute to damping of vibrations on ships: •	Material	damping •	omponent	damping. also to twice that frequency •	ompressors:	excitation	frequencies	are	equal	to	the	frequency	C of revolution and to twice that frequency •	earboxes:	excitation	frequencies	are	equal	to	frequencies G of revolution and meshing •	ropellers:	excitation	frequencies	are	equal	to	the	blade	P frequency and its multiples 24 . Thus. the damping grows with increasing fre-quency.13. For calculation of global vibrations. they can usually be split into harmonic components (excitation orders) with the aid of a Fourier analysis. According to the definition of the logarithmic decrement. e Λ corresponds to the amplitude ratio A1/A2 of two successive maxima in the vibration decay of a natural vibration mode excited by an impact force.g. For the higher frequency range in particular.	especially	that	produced	by	floor	C and deck coverings •	Cargo	damping •	Hydrodynamic	damping •	Mechanical	damping	(concentrated	damping) To characterise damping properties of a structure or a vibration absorber. There are clear descriptions in [24] and [25]. Hydrodynamic damping is generally regarded as negligible in the frequency range of ship vibrations. Excitation forces are introduced into the ship’s structure by a large number of machinery units: •	ain	engines	and	auxiliary	machinery:	excitation	frequencies M are half and/or whole multiples of the frequencies of revolution •	haft	machinery:	excitation	frequencies	are	equal	to	the	S frequency of revolution and. fluid. widely differing values are stated for damping characteristics in ship structural 4. in the context of the mode superposition method. each natural vibration mode has a particular damping coefficient assigned to it.13. it turns out to be difficult to measure modal damping coefficients since the mode density is high and natural modes can.). therefore. However. 18. e. b where ϑ = and c = stiffness.g. etc. impact excitation).13. From Λ = 0. bulk.
3. Orders transmitting free forces or moments to the hull must in all cases be regarded as significant. To obtain the total vertical force Fz. they can be calculated directly from the gas pressure characteristic by means of the formulas stated in [26]. This movement is transformed by the driving gear into a rotational movement of the shaft. In this way. Therefore. Fig. 19 depict the characteristic behaviour of various excitation orders during the start-up process of a six-cylinder two-stroke main engine. 4. 19: Waterfall diagrams for a measuring point on the ship and for one on the engine 25 . For a given rotational speed. since the force components occurring in various cylinders – summed over all cylinders with phase relationships taken into account correctly – cancel one another. nevertheless. the main engine of a ship introduces excitation forces into the foundation at all frequencies that are half and/or whole multiples (four-stroke and two-stroke engines. in computation practice. Forces in a single-cylinder engine For the simulation of excitation forces generated by slow-running main engines of ships. Thus. the inertia force of the oscillating masses must be superimposed on the contribution made by the gas force. i. In this paper. High vibration velocities can be expected only in those cases in which conspicuous excitation orders resonate with a natural vibration mode of the coupled system consisting of main engine and foundation. Theoretically. it is only in case of slowrunning main engines that the ship’s structure exhibits significant global vibrations caused by internal orders of excitation. 20. the engine structure of medium-speed and fast-running machines is not simulated for the purpose of considering excitation forces. internal orders of excitation do not transmit forces into the foundation. However. it was verified that they were stiffly connected to each other. but the other orders can also be recognised clearly. From the nearly identical behaviour of vertical accelerations at the measuring points on the engine’s bedplate and on the top plate of the innerbottom. One possible approach is to integrate a simple FE model of the housing into the computation model of the ship and to simulate the forces directly at the place where they originate. The most significant exciters here are those of the 6th. Measurement sensors were positioned on the engine bedplate as well as on the top plate of the innerbottom. the excitation effects stemming from propeller and main engine.1 Main Engine Basically.In addition. Normally. The waterfall diagrams shown in Fig. Forces acting in a single-cylinder unit are illustrated in Fig. 9th. there are some special types of vibration excitation. it is possible not only to cover the proportion of the internal excitation forces that produces an effect externally. in addition to gas forces. but also to take account of coupled natural vibration modes of foundation and engine housing (see Fig. global stiffness characteristics of the engine housing must be taken into account. do penetrate to the outside. As a result of combustion. only the main sources of excitation will be dealt with. such as periodic flow-separation phenomenon at structural appendages or torque fluctuations in electric engines.e. gas forces are produced which cause the piston to perform translational movement. The gas force acting on the piston in the vertical direction is obtained by multiplying the gas pressure with the piston area. To estimate the part of the forces introduced into the foundation by internal orders of excitation. respectively) of its frequency of revolution. both oscillating and rotating inertia forces are created. 14th and 16th orders. forces occurring within one cylinder are taken as the starting point. deformation-induced excitation forces. 12). because the stiffness of the engine housing is finite.
Fig. on the other hand. and let “dzk” be defined as the distance between main bearings and crosshead guide. If vibrations of the crankshaft or shaft line are to be considered. In the next step. Owing to the oblique position of the connecting rod. whereas transverse forces are acting at the centre of the crosshead guide and on main bearings. considering the ignition sequence. second and fourth order of excitation. Like the vertical force. vertical and transverse forces have to be considered. 20. The maximum vertical force is about 4. The engine housing is thus subjected to a periodic change of compressive and tensile forces of considerable magnitude. For reasons of equilibrium. vertical and transverse forces are applied – with the correct phase relations – to relevant nodes of the FE model of the engine housing. To judge whether excitation forces of the individual order are significant. Fig. 26 . both inertia forces and mean gas pressure change quadratically.200 kN. this does not apply exactly to individual harmonic components of the gas pressure. whereas a force of about 1.200 kW and a revolution rate of 104 r/min as an example. engine forces – formulated in Cartesian coordinates – can be converted to polar coordinates. The following table summarises harmonic components of vertical and transverse forces for the single-cylinder engine described above: Table 3 Ord. engine housing vibrations play the major role. this moment must equal (at ignition frequency) the torque generated by the tangential force. let “dxk” be defined as the distance of cylinder “k” from the centre of the engine. However. k and Fzi. Vertical forces are assumed to be acting on the top of cylinder units and on main bearings. 21 shows a schematical “snapshot” for a typical distribution of excitation forces of an engine housing. The characteristic of various force components is shown in Fig. so that the tangential and radial forces acting on the crank web pins are obtained. Thus. For revolution rates varying linearly. the following quantities can be defined for individual orders “i” of excitation. this inaccuracy is tolerated in return for a considerable reduction of data input. the equilibrium forces act. with the phase relationships being taken into account correctly.Fz is transmitted via the piston rod. The values quoted are valid for the revolution rate on which the calculation is based. In computation practice. connecting rod and crankshaft into the main bearings where corresponding reaction forces act. for instance. it is transmitted via the engine housing into the main bearings where. forces acting in their planes of effect are added over the length of the engine. Another advantage of this procedure lies in the simple method of taking account of irregular ignition sequences and in the possibility of simulating ignition failures. In the next step. in turn. the force curves shown are transformed into the frequency domain by means of a Fourier analysis. inertia forces 2553 3575 1712 875 1133 0 736 31 414 0 237 0 133 0 63 0 Fy [kN] Total force 508 165 37 144 101 54 37 23 The magnitude of excitation forces decreases with increasing order. k be the complex force amplitudes of order “i” acting on cylinder “k”. Influence exerted by the oscillating masses exists for the first. 20: Forces in the single-cylinder engine Naturally. Application of the Total Excitation Forces If forces acting in a single-cylinder unit are known for the individual orders. taking an engine with a cylinder power of 4. Let Fyi. The product of the transverse force and the current distance be-tween main bearing and crosshead gives the moment about the longitudinal axis of the engine. harmonic components of the tangential and radial forces are applied as sources of excitation. their phase relationship with other cylinder units can be calculated. see also [27]. 1 2 3 4 5 6 7 8 Fz [kN] From gas forces From osc.100 kN acts in transverse direction. If. a transverse force is created that affects the crosshead guide.
Whereas shaft line forces are the most significant factor for vibrations of shaft lines.k · dz k •	X-type	moment	(internal)	M X = ∑ F y – Gas i nk k=1 nk i. The choice of number of cylinders for a ship’s main engine is not based primarily on vibration aspects. nk •	H-type	moment	(external)	M D = ∑ F y – Gas i k=1 i. in turn. It is also necessary to consider whether the shape of the force distribution also corresponds to a coupled engine and foundation vibration mode. since no general statements can be made in this context. all excitation parameters can be taken from the engine manufacturers’ standard catalogues. are not taken into account in this table. •	Vertical	moment	of	inertia (external) M V = ∑ F z – Osc i nk k=1 · dx k i. 21: Typical excitation force distribution over the engine frame of a ship’s slow-running main engine 27 .3. Fig. installation of trans-verse stays also causes an increase in the H-type natural frequency of the main engine. However.k · dx k Except for the pitching moment.k nk •	Horizontal	moment	of	inertia	(external) M H = ∑ F y – Rot i k=1 i. transverse bracings may.The subscripts “Osc”. they are normally of minor interest as far as excitation of the foundation is concerned. However. the following table provides an indication for slow-running engines having 5 to 9 cylinders and the usual ignition sequences. Vertical moments of inertia and pitching moments mainly excite bending vibrations of the doublebottom in conjunction with an L-type vibration mode of the main engine. Horizontal moments of inertia and X-type moments cause torsional vibrations of the engine housing about the Table 4 Number of cylinders 5 6 7 8 9 Order of excitation 1st 2nd 3rd ⊗ – ⊗ – ⊗ ⊗ ⊗ ⊗ – ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ 4th 5th – ⊗ ⊗ ⊗ ⊗ ⊗ – – ⊗ ⊗ 6th – ⊗ – – ⊗ 7th ⊗ – ⊗ – – 8th – – – ⊗ – 9th – ⊗ – – ⊗ ⊗ Influence exists – Negligible influence Secondary sources of excitation. the danger of pronounced vibrations cannot be estimated on the basis of these values alone. excitation forces are transmitted into the ship via the shaft line and in the form of pressure pulses acting on the ship’s shell. result in unfavourable resonance situations with the H-type moment acting at ignition frequency. the predominant factor for vibrations of ship structures are pressure fluctuations. which orders of excitation may have a significant effect on global ship vibrations. However. especially axial force fluctuations that result from vibrations of the crankshaft and shaft line.k · dx k vertical axis.2 Propeller From the propeller. “Rot” and “Gas” indicate the physical cause of force effects (oscillating/rotating masses and gas forces). The recommendations of the manufac-turers to provide engines with a large number of cylinders with transverse bracings are mainly aimed at avoiding resonance with the X-type natural vibration modes. 4. Although excitations mentioned last can cause high vibrations in the transverse direction at the top of the engine.k · dx k •	Pitching	moment	(internal)	M P = ∑ F z – Gas i k=1 i. In the case of engines with six or seven cylinders and a revolution rate of about 100 r/min.
g. In practical applications.induced vibration velocities are caused by shaft line forces. In most cases. e. unsteady methods must be used. individual blade effects are superimposed.Shaft Line Forces Fluctuating shaft line forces result from the non-uniform wake. fluctuations in thrust and torque must be taken into account. Bending vibrations of the shaft are influenced by transverse forces in horizontal and vertical directions as well as by bending moments about the corresponding axes. The force fluctuations in transverse and vertical directions are between about 1 and 2% of the mean thrust. To obtain values for the overall forces and moments at the propeller. compared to fluctuations of the moment about the vertical axis and of the torque (5–20 % of the mean torque. both the thrust and the tangential force on the individual blade behave irregularly. this ratio is reversed. In this connection the computation effort needed and the available input data and deadline-related constraints should be well coordinated within the framework of the overall analysis. with the phase being taken into account correctly. When the shaft system is being designed.	D This effect is independent of the wake field. For computations of axial and torsional vibrations of the shaft line. periodically fluctuating moments also occur. and its contribution to the overall pressure amplitude for the propeller of a merchant ship is about 10 to 30%. The thrust fluctuation can be up to about 10% of the mean thrust. As a simplification. The phase relationship of the excitation forces cannot be considered reliably by quasi-stationary methods. a determination of the extent of cavitation is not necessary for the computation of shaft line forces. lifting-surface methods have won out in practice against procedures that simulate the lift effect of the propeller blade by means of a lifting line. Pressure fluctuations acting on the shell are a result of several physical causes: •	isplacement	effect	(thickness	effect)	of	the	rotating	propeller. compared to 1–10 %). as well as for the computation of the excitation effects for multiples of the blade frequency. The creation of these forces can briefly be described as follows: the relative velocity between the individual profile section of the pro-peller blade and the water depends on the superposition of the ship’s speed and the peripheral velocity at the profile section under consideration. fluctuating forces of the shaft line are only slightly affected by cavitation phenomena.7 R. In the design of vessels having propellers with weak cavitation. Fig. occurs independently of the wake field and contributes up to about 10% to the overall pressure amplitude. •	ortion	resulting	from	or	induced	by	the	pressure	difference	betP ween the back and the face of the blade. the moment fluctuation about the transverse axis is predominant. while at the same time the absolute excitation level is much lower. Since these forces act eccentrically at about 0. Therefore. the influence of the wake can be considered as the change in the angle of attack at the profile section. about 10% of propeller. this change being proportional to the inflow-speed variation. During each revolution. pressure fluctuations are more significant than shaft line forces. forces may excite various modes of vibration. for example. 28 . The quasi-static manner of consideration proves adequate only as long as the cord length of the blade profile can be regarded small compared to the wavelength of the flow disturbance. This effect. for which a certain degree of propeller cavitation is generally tolerated for the sake of optimising the propeller efficiency. whereas approximately 90% are due to pressure fluctuations. The simple computation methods are based on quasi-static con-siderations that determine thrust and tangential forces at the individual blade directly from the wake induced variation of thrust and moment coefficients throughout one revolution – see [28]. For this purpose. 22. In contrast to pressure fluctuations transmitted into the hull via the shell. As can be seen from the schematic diagram of the overall excitation in Fig. 22: Overall forces and moments at the propeller Pressure Fluctuations Regarding excitation of ship vibrations. but it is usually between 2 and 4%. Because of the computing powers available today. the geometric data of the propeller are usually not available with the degree of detail necessary for the computation of excitation forces by a lifting-surface method. In merchant ships. the method described in [29]. this condition is fulfilled only for the blade frequency. too.
but instead the volume curve is rendered uniform by the offset in the circumferential direction. Both processes are excitation phenomena that. developed at the Hamburg Ship Model Basin (HSVA). Principally. Normally. the latter phenomenon mainly influences the excitation characteristics in the noise frequency range. the contribution of this effect to the overall pressure amplitude is approximately 60 to 90%. However. In addition. For the propeller of a merchant ship. [35] and [36]. at present. the propeller can also generate excitation effects with frequencies differing from multiples of the p = ρ 1 ∂ 2V · · 4π r ∂t2 where ρ = fluid density. an appropriate correction can be made in accordance with [34]. for example. Some concepts tolerate comparatively severe cavitation phenomena. for example. In the following. Whereas the former process mainly has an effect in the frequency range corresponding to the higher harmonics of the propeller blade (see [30]. The corresponding computation methods can be divided into empirical. However. for example). Pressure pulses on the shell are also caused by the induction and displacement effect of the propeller tip vortex and the collapse of the individual cavity bubbles. is carried out by means of empirical formulas. With software based on [29]. Here the determination of the expected cavitation volume curve is performed with the aid of a numerical approximation process based on vortex distribution. the pressure amplitude is governed by the curvature of the volume curve. the latter calculation step. Exceptionally. a situation can be achieved where the individual profile sections of a propeller blade are not all subjected to their maximum loading at the same time. this curve can be estimated by calculation. If this is not the case. the volume curve should exhibit the smallest possible curvatures. the curve of the cavitation volume versus propeller blade position must be known. For high-skew propellers. One semi-empirical method is the Quasi-Continuous Method. by means of skew. The flow condition in the tip region of the propeller blades has a particularly strong influence on cavitation phenomena. A comparison of results obtained from empirical and semi-empirical methods with full-scale measurements is dealt with in [37]. improved cavitation characteristics must normally be “paid for” by reductions in efficiency. To derive the pressure amplitude from the formula stated above. unusual characteristics of the propeller may be the cause. propellers having a high skew are not covered by these statistics. More advanced methods should be reserved for novel designs where a higher computational effort is justified. and are aimed at making the growth and collapse of the cavitation layer as slow as possible. As described in [31]. these special aspects will not be dealt with. is performed using a numerical approximation method. too. i. The magnitude of this effect depends on the geometry of the ship’s hull and must be determined separately. The formulas given therein are based on regression analyses of data determined with a large number of full-scale measurements. both in the radial and circumferential direction. the quantity to be used is the second derivation of the cavitation volume curve. If the aim is solely to determine the pressure fluctuations for a standard vibration analysis. However. The pressure amplitude is thus proportional to the acceleration of the volume of the cavitation layer. empirical methods are often still preferable. namely the calculation of the pressure amplitude from the cavitation volume for a given geometry of the ship’s shell. The formula stated above characterises the principal mechanism of creation of pressure fluctuations. The flow condition at the blade tips is additionally complicated by the formation and subsequent detaching of tip vortices. The following step. by model experiment or by full-scale observation. pressure fluctuations decrease for higher blade harmonics. for example. This can be achieved by influencing the wake (minimising wake peaks) and by a suitable choice of propeller geometry. semi-empirical and numerical procedures: The method presented in [33] is a purely empirical procedure where the pressure amplitude is determined from a small amount of geometric data related to the propeller as well as from the wake. The formula is applicable for the free field and does not take account of the obstructing effect of the ship’s hull. Calculation of the volume curve requires knowledge of the pressure distribution on the propeller blade. From the above-mentioned contributions to the overall pressure amplitude. Selection of a larger area ratio Ae/A0 and reduction of the propeller tip loading by selection of smaller pitch and camber at the outer radii are the most effective measures. An evaluation of the two methods is described in [38]. see [32]. but it is not suitable for the actual prediction. it can be concluded that high excitation forces can be expected only in case of cavitating propellers.e. Computation programs for the prediction of cavitation volumes are correspondingly complex. 29 . are scarcely amenable to methods of calculation and should – if necessary – be investigated in a cavitation tunnel.•	Displacement	effect	of	the	fluctuating	cavitation	layer	that typically forms when the propeller blade is moving through the wake peak in the region of the outer radii. pressure pulses caused by a fluctuating cavitation volume V at a point situated at a distance r can be approximated by the following formula: To avoid strong cavitation-induced pressure amplitudes.
no generally valid limits can be stated for pressure fluctuation amplitudes. Furthermore.induced contribution (approximately in proportion to 1/r2. The number of propeller blades does not have any marked effect on the magnitude of pressure fluctuations.4 Evaluation and Assessment A complete investigation of the vibration behaviour should involve not only an examination of the local structures for the danger of resonance (see 3. etc. Whether these considerable excitation forces result in high vibrations depends on dynamic characteristics of the ship’s structure. integrated from pressure fluctuations. 23: Propeller-induced pressure distribution at the frame cross section 4. two differences are pointed out between pressure fluctuations induced by propeller blade thickness and those induced by cavitation: •	he	thickness-induced	contribution	decreases	much	faster	with	T increasing distance from the propeller than the cavitation. This generally indicates transient phenomena occurring in the ship’s wake. pressure fluctuations must be integrated over the immersed part of the aftbody shell. As known from experience. and can only be judged rationally on the basis of a forced vibration analysis. 23. i. Total vertical force fluctuations at blade frequency. but also a prediction of the vibration level. but also on the geometry-dependent compromise between efficiency and pressure fluctuation. fluctuations are almost in-phase throughout the entire region affected Superimposition of the two contributions is shown schematically in Fig. corresponding values lie in be-tween 100 and 300 kN. These amplitudes depend not only on technical constraints (achievable tip clearance of the propeller. Therefore. some possibilities for a corresponding evaluation of calculation results of forced vibrations are described. the pressure amplitude above the propeller alone is not adequate to characterise the excitation behaviour of a propeller. In this connection. For optimisation of a design from the vibration viewpoint. “medium” and “high”.blade frequencies. 30 . Predicted amplitudes can then be compared with limit values specified for the ship concerned.	phase	relationships	I of the cavitation-induced pressure fluctuations change only insignificantly with increasing distance from the propeller. In the following.000 kN for a high-performance container vessel. As a result of the differences mentioned.5 as opposed to 1/r) •	n	contrast	to	thickness-induced	amplitudes. range from about 10 kN for a special-purpose ship to 1. a number of design alternatives can be checked.). using results of forced vibration analyses for various variants. To obtain overall excitation forces. respectively. For usual ship types and sizes. Nevertheless. variant calculations are to be recommended as part of the evaluation procedure. Fig.e. for which the cost of calculations is almost negligible compared to potential savings. pressure amplitudes at blade frequency of 1 to 2. Decisions to be taken include the following: •	ow	many	propeller	blades	are	to	be	recommended? H •	re	mass	moment	balancers	necessary	to	achieve	the	agreed	A vibration	level? •	o	engine	supports	(transverse	or	longitudinal)	improve	or	D worsen	the	vibration	behaviour? •	ould	it	be	advisable	to	provide	a	damping	tank? W •	ould	structural	modifications	be	advisable? W For large series of ships. 2 to 8 and over 8 kPa at a point directly above the propeller can be categorised as “low”.3). evaluation methods that reflect the spatial distribution of vibration velocities for individual excitation frequencies proved to be helpful. taking account of phase relations. the cavitation effect on integrated overall forces is even more predominant than is already the case due to the significant influence on pressure fluctuations. power to be transmitted.
a judgement can be conducted directly according to the old ISO 6954 standard as described in section 2. for each excitation order and location. calculation of amplitude spectra has proven its worth in practice. definite natural frequencies can be assigned to the 2nd order curve. because the vibration response determined can then be attributed to a definite cause.4. Fig. vibration velocities are calculated for about 200 excitation frequencies within the selected frequency interval to obtain sufficient resolution of the curve shape. calculation and measurement. which natural vibration modes make a significant contribution to the system’s response. Therefore.1 and 3. The upper diagram applies to excitation by the 2nd order of the main engine (external vertical mass moment) and the lower diagram refers to the 7th order fluctuation of torque (ignition frequency).1 in the case of main engines. An assumption is then made about the dependence of excitation forces on the frequency. e. If the mode superposition method was used for the calculation of forced vibrations. Vibration velocities determined during full-scale measurement are likewise shown (curves with markings). Vibration velocities (peak values) in longitudinal (x).1. A determination of the vibration response over the total frequency range for all nodal points of the FE model is not possible in prac-tice. In contrast to the 7th order. Normally. the curve for the 7th order is more balanced.m. This may be due to inaccuracies in the calculation. a particular revolution rate has not been specified. it is possible to state. 24: Velocity spectra for excitation by the 2nd and 7th orders of main engine excitation Excitation forces are generally determined for a reference rate of revolution. it is assumed for the sake of simplicity that excitation forces are proportional to the square of the revolution rate. Calculated natural frequencies are about 5% higher than measured ones. For this kind of presentation divisions on the frequency axis can be selected freely.3. The lower and upper limit lines as per the old ISO 6954 are highlighted by horizontal lines. In this case.s.0 Hz can be identified. in many cases. assumptions about the dependence should be chosen with care. Fig. or to the use of slightly different draughts in the calculation and measurement condition. Especially for the evaluation of amplitudes determined for excitation frequencies differing more markedly from the reference revolution rate. predicted vibration velocities at a stiffly supported (global) point on the bridge deck of a container ship is shown. 31 . Since natural frequencies vary for different loading conditions and also because. The curve characteristic of the 2nd order excitation differs greatly from that of the 7th. Whereas for the 2nd order there are definite maxima. nor is it necessary. indicate the larger mode density in the higher frequency range. respectively. 24 shows two typical vibration velocity spectra.1 Vibration Velocity (Response) Spectra It is recommended to perform the calculation of forced vibrations separately for relevant orders and sources of excitation.g. This form of evaluation is generally per-formed for a maximum of about 50 representative points of the ship’s structure. Both. the nominal revolution rate or the revolution rate during the acceptance measurements. and the determination of overall frequency weighted r. As already explained in 4. and transverse (y) directions are plotted logarithmically for a range surrounding the nominal revolution rate. values according to the new standard can be derived from amplitudes calculated for individual excitation orders. Furthermore. One principal advantage of this kind of diagram is that trends on the amplitude level for varied natural and excitation frequencies are illustrated. On this basis most effective meas-ures for detuning these modes can be specified. The latter is indicated by a vertical line in the diagrams. vertical bending vibrations of the ship’s hull at 2.4. Here. investigations should be carried out over a large frequency range.
turned out to be useful. Because deck grillages are taken into account in the FE model with the aid of beam elements. Fig. At the 3rd order (4. All revolution rates that have a predominant effect on ship operation should be investigated.0 Hz) mainly excites longitudinal vibration of the engine. The length of the arrows indicates the vertical velocity at the node concerned. The outer starboard panel behind the fourth transverse bulkhead. In cases of this kind.5 Hz) excites the fundamental torsional vibration mode of the ship’s hull. respectively. The excitation is caused by the external fourth-order mass moment and by the pitching moment. This kind of evaluation makes it possible to draw conclusions about the interaction between excitation forces and natural vibration modes.2 Velocity Distributions It is not possible to derive the spatial distribution of velocities from the response spectra predicted for a few selected points of the ship’s structure. there are two such states.3 Mode of the Forced Vibration Another clear illustration is a plot showing the spatial shape of forced vibrations. The 4th order (6. resonance with the L-type vibration of the housing can lead to a considerable increase of excitation forces. Torsional vibrations of the aft part of the ship can clearly be identified. practically no vibrations are transmitted into the foundation. When reaching the aftmost hold bulkhead. In the example shown. the vibrations largely decayed. uncritical in spite of the resonance situation. Highest vibration velocities occur in the transverse direction at the top of the engine. This particular example involves the aft region of the main deck of a naval vessel. In this case. too. only a limited statement can be made about local magnifications of vibrations from these spectra. which is likewise conspicuous at this order.4. Because the fundamental natural torsional frequency of the deck- Left arrow: : Vibration velocity (vertical) Operating Condition 1 Right arrow: : Vibration velocity (vertical) Operating Condition 2 Fig. Especially for passenger and naval vessels with complex spatial structures. the vibrations are excited by the propellers. 25. a definite increase can be seen in the vibration of the housing compared to the doublebottom. for instance. The 1st order (1. In particular. combined with longitudinal vibration of the deckhouse.5 Hz). showing the velocity distributions over a deck. a diagram as presented in Fig. the panel is.4.4.0 Hz) causes four-node vertical bending vibrations of the ship’s hull. 4. 25: Vibration velocity distribution in the deck area 32 . As explained in [27]. especially when trying to balance between the achievable improvement of the vibration behaviour and the effort required for such an improvement. The shipyard can benefit from such diagrams. There is no recognisable increase in the longitudinal vibration of the engine. therefore. The vibration level decreases from aft forwards. whereas the vertical second-order mass moment (3. is obviously in resonance in case of Operating Condition 1. Because of the high stiffness of the structure and the large distance from the source of excitation. 5th and 6th orders of excitation cause a similar vibration mode as the 3rd order and are. it is mainly the X-type bending moment of the engine that takes effect. not shown here. nevertheless. The 7th order of excitation (10. 26 shows forced vibration modes for the excitation of the ship’s hull by various orders of a sevencylinder engine. In this case.5 Hz ignition frequency) evidently causes H-type transverse bending vibrations of the engine housing. indicated by the left and right arrows. it is also possible to identify local increases of vibration. there is some elbow room for the decision as to whether further stiffening measures are advisable. Because this is an internal moment and the stiffness of the engine housing is adequately high.
33 . which is almost impossible to detect with simpler methods of calculation and evaluation. 26: Vibration modes in the case of excitation by vibration orders of the main engine 7th order house is close to the excitation frequency. because the calculation of forced vibrations of ships requires a considerable amount of numerical effort. is to find a reasonable compromise between cost and benefit. A computer animation of forced vibration modes provides further important information and indicates potential improvements. too. Deckhouse and engine vibrations couple in a complex mode. However. a large number of evaluation algorithms can be used. Naturally.1st order 2nd order 3rd order 4th order Fig. the challenge here. the bridge deck reveals high amplitudes.
together with efficient software. occur for a novel design as a consequence of poor inflow to the propeller. A brief overview of sensors and measurement systems used for vibration analyses is given below. this triggering possibility can be extremely useful. are difficult to identify since their occurrence often depends on specific. Moreover. which are becoming more and more detailed and hence require an increasing amount of effort. For example. permit the configuration and evalu-ation of even the most demanding and extensive experimental investigations. For structures typical in shipbuilding and marine engineering. many investigations that even ten years ago were the domain of research can now be carried out within a reasonable time and almost as a matter of routine.This has led not only to devices that are now portable and comparatively user-friendly (of the “plug & play” variety). and in most cases they are distinctly lower. only the frequency range up to about 300 Hz is of interest from a vibrational point of view. but initially unknown. length to beam. for example.g. In this connection. on the one hand. On the other hand. or because air is getting underneath the ship at its forward shoulder. but also to computing powers of PCs or workstations that. 5.1 Sensors In any application. Thus. In such cases.) are disappearing more and more from the design process. six specific examples from practical work (troubleshooting) indicate how special vibration problems on ships can either be avoided or solved at comparatively low cost. such as fins. Specially worth mentioning are “pre-triggering” and “post-triggering”. Corresponding problems can only be solved by a well-planned measurement campaign. The dis-advantage of processing the huge and bewildering amount of measuring results collected over months can thus be avoided by pre-selecting relevant data. This is followed by an introduction to the procedure of various measurements frequently applied in shipbuilding and ship operation. production optimisation and the trend towards uncon-ventional designs and new hull forms require an increasing demand of measurement. The problems selected are technically simple. Every manufacturer offers a wide spectrum of standard sensors constituting an ab-solutely vast range to choose from. conventional ratios (e. Popular sensors consist. Finally. etc. Specific excitation phenomena may. conditions. Some typical methods to evaluate measurement data and to assess results are discussed next. beam to draught. but in some cases they had serious economical effects. Further reasons for an increasing use of experimental investigations in ship technology include the general trend towards lower structural weight combined with increasing propulsive power. resulting in unpredictable vibrations. As spring-mass systems they also measure statically (0 Hz) and function as inclinometers. Measurements In parallel with the progress being made in the field of vibration prediction with mathematical models (FEM). of seismic types.5.. The maximum acceleration values are generally less than 1 G. flow-induced excitation forces transmitted into the ship’s structure via appendages. by means of which even rare events can be measured automatically in a purposeful manner with almost all multichannel measurement systems. One of the main reasons for this is undoubtedly the general progress being made in electronics. The latter offer advantages in the high frequency 34 . nozzles or rudders. The individual problem and the way it was satisfactorily solved on the basis of measurements can be clearly understood from the presented graphic presentations. a growth in the use of experimental investigations is also evident. accelerometers are essential. piezo-electric sensors are widely used.
containing amplifier boards often integrated in the housing. For vibration investigations on board ships they are necessary only in exceptional cases. equipped with 32 or 64 channels and extensive triggering features. however. 5. If data quantities are small.range. with up to 2 hours capacity. The configuration of measurement channels and other setting activities.to 4-channel system. 1. the time signal is mostly not available.to 4-channel systems consisting of sensors. on hard disks. take place via the interface connection to the PC or laptop.g. this corresponds to a vibration velocity of approximately 0. Depending on the requirements. such as those for trigger functions and for controlling the measurement procedure. for reasons of memory capacity. For measurements of propeller pressure fluctuations. consequently. At the next level. such as 2-channel analysers or thermal printers for checking and observing the measurement. and then because of their trigger functions. the measurement chain corresponds to a 1. 5. play a part in special cases only. experience has shown that clear definition is difficult since the decision has also to be made for unknown future tasks. The analog amplifier output (generally with a maximum of 2. In the conversion of analog to digital data. possible aliasing effects must be taken into account.. therefore. These effects can generally be ruled out if analog signals are suitably filtered. To name an order of magnitude: 5 mm/s2 (about 0. laptops can be used instead of a DAT recorder. there are 8. for long-duration measurements – and are mentioned here only for the sake of completeness. the upper frequency limit ranges to about 10 kHz or even higher and thus can also cover the structureborne noise range. “front-end” units as they are called. Basically. The range comprising 16 or more channels is the domain of complete data acquisition systems. they are unsuitable for measurement of ship motions below 1 Hz. a reasonably rational decision in favour of a specific system is possible only if the measurement task is clearly defined. In the simplest case. DAT cassettes or MO (magneto-optical) disks. dynamic range and sensitivity are likewise comparatively easy to fulfil nowadays. Depending on the design. extensive meas-urement data are stored on the PC hard disk or via external drives. Sensors for the direct measurement of vibration velocity. On the other hand. These units can certainly not be classed as “mobile”.g. However. which is predominantly the quantity to be assessed. be bene-ficial. Also. requirements to be met by sensors with regard to pressure range. amplifiers and a DAT recorder can still be classed as “mobile”. e. because of the physical principle on which they are based.. battery-powered) and easy-to-operate single-channel compact devices up to PCcontrolled multi channel measurement systems.to 16-channel units. This requires. A greater ruggedness to cope with possible influences in the vicinity of a propeller (such as sand or unfavourable cavitation effects) to re-liably withstand prolonged investigations would. the use of a wide variety of sensors. DAT cassettes. Equipment with this scope is typical for investigations of the global vibration behaviour. which require a place in a protected environment and a 220 V power supply. For the widespread need to determine the vibration level at various places on the ship and to clearly identify the main source of exci-tation. and hence the possibility of automatically measuring vibration phenomena that rariley occur. of the engine).3 Measurement Procedures Depending on the kind of problem and the measurement effort to be expended.0005 G) can be measured without any problem.	Unfortunately.g. of the aft part of the ship including the deckhouse as part of the troubleshooting process. To detect causes of special vibration problems. The sensitivity of both types of sensor is adequate for the measurement of mechanical vibrations. the vibration measurement procedure must be adapted to suit the given operational constraints. 5 or 10 V) make it possible to connect other devices. at the limit of the human perception threshold. 35 .2 Measurement Systems The production lines range from handy mobile (i. In view of the wide variety of devices available. At a frequency of 10 Hz.08 mm/s and is. e. There is no such thing as a practical device for all possible applications. a higher-performance and more compact generation of the product will generally appear on the market after a few years.	they	do	not	yet	feature	evaluation procedures as per the new ISO 6954. However.e. represent the upper end of the scale. Evaluation takes place later with a PC using appropriate software. not only piezo-electric elements but also strain gauges are used. it is sufficient to use single or dual-channel frequency an-alysers in hand-held format capable of showing the measured spectrum on a	small	display	and	to	store	it. These systems make it possible to program a completely auto-matic measurement procedure – for example. are a worthwhile stor-age medium.. Measurement data are then present in digitised form on the hard disk at a defined sampling rate. and they have the advantage of being able to record time signals simultaneously in a practically unlimited manner. it is occasionally necessary to measure various operational parameters (e. These advanced systems. As measurement cells. a distinction can be drawn between measurements for various excitation types.
3. therefore. and both functions should remain stable.to 3-channel device.3. results have to be corrected in accordance with hydrodynamic masses. i. changes at this time are still com-paratively cheap for the shipyard. too. For this purpose. the vibration level is caused by slamminginduced impacts or by special flow phenomena. For upper superstructure decks transverse and longitudinal directions should be considered as well. Furthermore.e. on which generally two to eight accelerometers have been attached beforehand by means of magnets. The selection should cover various sizes of panels and positions on the deck for measurements in the vertical direction. moderate wave heights. since they do not provide information either on natural frequencies or about vibration modes. if problems exist.3 Measurements During Ship Operation Here. but the necessary conditions cannot be realised on a sea voyage in the near future. which reflects the most important operating condition of a ship. it is sufficient to check or record about 20 measurement points distributed over superstructure decks and workshops. 5. The fixing of the exciter foundation requires a certain amount of construction work. they are often possible only on weekends. In individual cases. small rudder angles. As a result of the impact. larger panels. then the task has been completed with a minimum of effort. on the other. This method is also used when vibration problems occur. The expected vibration level is then extrapolated from the measured level. various orders of the propeller and engine. on the one hand. In addition. Therefore. In this case.5. these measurements are generally not sufficient to clarify causes. for example. They are mainly used to check the design of plates. In case of passenger ships. a mistake here would be particularly critical. it is scarcely possible to develop a detailed diagnosis with the aim of working out effective remedies. Special attention must be paid to turbochargers.2 Exciter Test In this case. the component is deflected locally and performs decaying vibrations at its natural frequencies. However. indicate when the measurement can be discontinued. In the case of a newbuilding. This requires an adequate water depth (four to five times the draught to eliminate shallow water effects). it must be estimated beforehand whether the frequency range and the excitation force are adequate for the vibration problem. for example. The coherence should be near unity over the frequency range of interest. i. the aim is mainly to determine natural frequencies. panels and stiffeners of superstructure decks and tank walls in the engine room area before the ship is completed. using a hand-held or a 1. Small unbalance exciters (Fmax < 100 kN) are highly suitable for the investigation of appendages. an attempt is made at an early stage to simulate ex-citation characteristics of the engine or propeller by means of an unbalance exciter test. Coherence and transfer functions.1 Impact Method The purpose of these measurements is to determine natural frequencies of particular structural components or equipment items. The structure concerned. taking excitation forces of the engine or the propeller into account. these investigations require a work pause during construction which is not always easy to arrange. 36 . If limits are not exceeded and the vessel’s master and/or the owner indicate that they are satisfied. when a high amplitude level was predicted. More powerful exciters require extensive installation effort because of their great weight and their dimensions and are. In rare cases. continuously monitored on an FFT analyser. Therefore. or foundations of larger items of equipment. 5. they should not change when further impacts take place. engines and peripheral devices are subject to limits that must not be exceeded if damage is to be avoided. for example. the ship’s own vibration sources provide the excitation forces. Only then can an informative overall picture be obtained. is struck non-rhythmically with an impact hammer. and the absence of violent ship motions. is applied to compare the measured vibration level with permissible values stipulated in the building specification. Measurements at Rated Output of the Propulsion Plant This measurement procedure. used in exceptional cases only. individual decks. and the guarantee that damage to the structure is avoided. If measured natural frequencies indicate a danger of resonance with main excitation orders (propeller and engine)..e. The hammer has a suitable rubber buffer at its impact surface and is additionally equipped with an accelerometer for measurement of the striking force (the weight of the hammer being known).3. A further field of application is the investigation of structures and appendages situated below the waterline.
however. To determine the hull’s basic vertical natural modes and frequencies.	Unacceptable	global	vibrations. it is still comparatively time-consuming to go through all time series and to check whether they meet expectations. [39] and [40]. permits not only the determination of relevant vibration modes: when combined with a run-up manoeuvre of the propulsion plant. Measurement durations of up to 5 minutes for quasi-steady state conditions (constant speed and propeller pitch) make it possible to distinguish between excitation frequencies.g. These signals are present either in digital form in bulk memories. in the range 50–100% of the nominal revolution rate. 37 . to move the four sensors placed on the bridge deck to one side of the main deck. both the sampling rate (the highest signal frequency) and the measurement duration (frequency resolution) should be chosen generously. one vertical) usually reflect with sufficient clarity global vibration modes of the deckhouse (longitudinal. e. Basically it can be stated that local problems (“calming” of panels. They are.g. for example. even if they lie close together. for example. not only the revolution rate but also the pitch should be varied in the range of 50–100 % to assess cavitation phenomena. or in analog form if magnetic tape units are used. Frequencies cut off by the digitisation process are irretrievably lost unless the original signals are stored on magnetic or DAT tape. it is sufficient. The measurement data then permit an identification – possibly supported by calculations – of cost effective measures. or smaller equipment items) can be solved with	little	effort.. bulkheads. e. 5. 3 or 5 revolutions – a total duration of 20 to 40 minutes must be expected if no resonance points in the relevant range of revolution are to remain undetected. devices. In case of largely unclear vibration problems. The sensors and the sampling rate define the highest frequency still contained in the signal.	on	the	other	hand. also appropriate if shipyards or owners attempt to reduce the vibration level or if they want to find out why an engine top bracing. MO disk. it is only possible by means of pressure pulse measurements to determine whether induced pressure fluctuations are unusually high. torsion about the vertical axis).	require considerable modifications of the design or of the propulsion plant – extending in extreme cases up to changes of the revolution rate or of the number of propeller blades. transverse. The reason is that. DAT tape or CD. On the other hand. 5. one transverse. Combined with sensors in the vertical direction at the forward and aft footing of the deckhouse and at the transom. even with the insight of an experienced engineer. for example. For example four stiffly supported measurement points on the bridge deck of merchant vessels (two longitudinal. An alternative is offered by popular DAT recorders.4. it is necessary to have measurement data available as time signals. Accelerometers can easily be moved from one position to another. possibly together with other measurement quantities. If the propeller has been identified as the cause of a vibration problem.1 Time Domain Assessment of the time signal itself is often neglected in favour of powerful statistical procedures and compact analysis methods in the frequency domain. in case of speed-up manoeuvres – either continuous or in small steps of. relevant natural modes and natural frequencies of the whole elastic system consisting of deckhouse and aftbody can be determined. results also reveal relevant resonance points showing corresponding natural frequencies. The measurements sketched represent the scope typically required for troubleshooting. but have finite data rates. In the case of controllable pitch propellers. has failed to produce the hoped-for success. Theoretical background of various evaluation methods is dealt with in standard works. which behave like analog devices (voltage output). say.Measurements at Variable Revolution Rates The simultaneous acquisition of 8 to 16 acceleration signals.4 Evaluation and Assessment For various possibilities of data evaluation. such as hard disk.
if the time signal of a particular frequency is of interest. caution is advisable because FFT parameters. Multichannel measurements permit the determination of complicated vibration modes and associated amplitudes. steady-state or transient. especially as a result of many components having different amplitudes and frequencies. even in the case of measurement intervals in minutes range. e. These spectra likewise form the basis for assessment according to various technical standards – see also Chapter 2. spectra reveal the amplitude level corresponding to each frequency. For assessment. Only time-consuming piece-by-piece integration can then lead to success. The reason for this lies in the constraints of the electronics of sensors and other devices. therefore.However. Furthermore. The shape. of propeller blade frequency. However. Typically. Time signals provide valuable clues for an understanding of the vibration problem – clues which other methods are unable to supply.2 Frequency Domain Spectral analysis based on the Fast Fourier Transformation (FFT) is by far the most powerful tool for assessment of vibrations. makes clear whether time signals are periodic. structures. and thus make it possible to identify main excitation sources. a time signal is extracted that then represents the vibration created by the propeller blade frequency only. Even though vibration signals are often stochastic and transient in their nature. 5. integration of the acceleration signal causes difficulties.g. engines and electronic equipment do not only differ from each other in permis-sible amplitudes. as far as amplitudes are concerned. However. This method identifies main sources of excitation immediately on board. trim and list change the mean value. low-frequency motions of the ship are reflected in vibration signals where specific sensors are used. immediately provides information as to whether steady-state conditions exist or time intervals are occurring with widely differing amplitude levels. occasional faults such as signal gaps or the occurrence of peaks only have a slight falsifying effect on the result. can have a significant effect. The usual evaluation software basically makes it possible to per-form differentiation and integration in the time domain. covering the entire measurement duration. A time plot. vibration standards for comfort. the result often remains unsatisfactory. they also require widely differing evaluation methods. harmonic analysis is. filtering can be used as an aid. 38 . unpleasant beating effects become clear immediately. the vibration velocity signal is often desirable. Of course. several orders of excitation determine the vibration level on board. For example. The time signal can. nevertheless. However. block sizes and overlap. By elimination of the unwanted frequency ranges. such as windows. Several signals recorded simultaneously indicate phases and amplitude relationships when grouped below each other or arranged in a common mesh. Even if the mean value (and possibly also its trend) is eliminated beforehand. If the quantity of data is large enough. first of all.4. Additionally. evaluation of some typical time series is advisable. become complicated and hence scarcely capable of interpretation. generally successful. Amplitude Spectra In the selected band. harmonic or stochastic (random).
etc. but are also able – in conjunction with FEM programs – to simulate effects of changes in the structural model (stiffness. but it can also be the propeller pitch while the speed remains constant. unbalance exciter units. Depending on mass and stiffness relationships. Naturally. knowledge of the causal vibration mode is crucially important because it is only on this basis that effective countermeasures can be worked out. excitation of a hull’s natural vibration modes does not require a “suitable” sea state in the sense of a particular wave encounter frequency or particular pitching motions. mass characteristics) on results. In the event of vibration problems. important to proceed with a specific purpose in mind during measurements.Waterfall Diagrams “Waterfall” diagrams (three-dimensional spectra) additionally indicate the change of amplitude and frequency versus time. It is. On the other hand. it must not be forgotten that this kind of speedup manoeuvre also affects quantities influencing the vibration behaviour. The two-dimensional presentation shows the variation of amplitude as a function of frequency in a convenient manner. for example. wave heights of. Lower natural frequencies of the hull’s bending vibrations (vibrations with two to four nodes) are generally revealed. the main parameter is varied either as uniformly as possible or in steps. specific excitation arrangements to determine a hull’s natural vibration modes require great effort (anchor-drop test. for example. which might result in undesirable effects. natural vibration modes are independent of the revolution rate. impact systems. Even with a 32-channel measuring equipment. Knowledge of vibration modes acquired from FEM computations. In most cases. the use of modal analysis in practice is mostly confined to parts of structures or individual items of equipment. so that phase relationships between individual measurement points can be considered. Order Analysis This term refers to the relationship between amplitude and excitation frequency for a particular order of excitation. As described in some of the practical examples.. can be helpful. among others. Corrective measures are generally aimed at 39 . damping. stopping manoeuvres. A necessary prerequisite is simultaneous acquisition of signals. In practice. detecting global vibration modes requires much effort. 0. shock tests. it would be useless to provide a strongly vibrating deck panel with supports situated at nodes of the vibration mode causing the disturbance. for example.). Thus. This can also apply to larger subsystems. Modal Analysis This is generally regarded as a tool to determine vibration modes (free and forced) of complex structures by means of a large number of measurement signals.5 m are sufficient to excite these natural vibration modes to an extent that amplitudes and corresponding natural frequencies can be measured. the spatial vibration mode can be measured for only limited areas of the hull. For this reason. In this connection. Over a period of 20 to 40 minutes. e. waterfall diagrams conspicuously reveal existing resonance points. In addition. Today.g. such as a deckhouse or a radar mast. Contrary to common assumptions. coupling of this kind also changes the vibration behaviour of the adjacent part of the structure. program packages for modal analysis not only offer the possibility of displaying detected natural modes as animations on a PC screen. relevant excitation forces and ship’s speed increase during this speed-up process. connecting structural points characterised by large relative motions. In a waterfall diagram it corresponds to the mountain ridge. The former represents forced vibrations and can be assigned directly to the nth order of the engine or to the propeller excitation. amplitude curves varying with the engine speed can be distinguished from those in which the frequency remains completely invariable. hydropulsers. therefore. This parameter is principally the speed of the main engine and hence of the propeller. For large ships.
depending on the position of the vibration node relative to the balancer force. at only one end of the 6-cylinder engine. If the balancer acts at the node. However. In addition to resonance of the mast at propeller blade frequency. 27: Waterfall diagram for the longitudinal acceleration of the bridge deck 40 . In addition to severe vibration problems of some local components on the radar mast.83 Hz.5 Practical Applications Example 1 The first unit of a new series of container ships was investigated because of significant vibration problems on a loading voyage. The radar mast reached amplitudes of more than 30 mm/s. This was particularly critical because it was the service speed with the shaft generator switched on. were unacceptable. resulting in torsional vibrations about the vertical axis. The vibration behaviour in ballast condition was found to be as unfavourable as in loaded condition. In the waterfall diagram of Fig. It was found that the shipyard installed a compensator. The shipyard initially hoped to reduce deckhouse and mast vibrations to an acceptable level by carrying out various structural alter-ations (stiffening of the radar mast. caused by the propeller blade frequency (4th order). the position of the relevant vibration node can move considerably. The radar mast. driven at twice the revolution rate. an increase of vibration is even possible to occur in the worst case.5. A one-sided configuration of this kind gener -ally produces incomplete compensation. corresponding to 3. high global longitudinal vibrations of the deckhouse. Fig. reached the largest amplitudes at a maximum revolution rate of 140 r/min. on the other hand. The installation of a balancer acting at one end only. must therefore. whereas in the loaded condition resonance with the 5-node vibration occurred at about 126 r/min. These were due to asymmetries of the deckhouse. 27. in particular. Depending on the loading condition. with values of up to 12 mm/s. no change occurs in the vibration level. changing of the deckhouse asymmetry). it turned out that significant vibration problems still existed and that the limit curves specified were not being complied with. An evaluation of the 2nd-order excitation at 115 r/min. Evaluation of the first course of remedial action revealed the following situation: In the deckhouse (at the height of the bridge deck) there was a level of about 9 mm/s due to the engine’s 2nd-order excitation. exhibited proximity of resonance to the 4-node vi-bration of the ship’s hull in ballast condition. The port side exhibited higher vibration velocities. Because the phase relationship of the compensator force is fixed. the main reason for the high level turned out to be resonance of the four-node vibration mode of the ship’s hull with the engine’s 2nd-order excitation. the resonance for the longitudinal vibration of the deckhouse is clearly evident for ballast condition. be regarded as critical. as a means of compensating a free 2ndorder mass moment. The highest level of longitudinal vibration of the deckhouse occurred at engine speeds of about 115 r/min.
3 Hz). to the forward edge of the wheelhouse deck.35 Hz and 2. Fig. As a result. Sister ships were finally fitted with balancers at both ends of the engine as standard equipment. Time signals from various measurement points are shown in Fig. 31. bridge deck. The vibration behaviour of the mast in the longitudinal direction is illustrated in Fig.. 29: Amplitude spectra of vibration velocity. The crew reported extreme vibrations in the deckhouse area in bad weather. It was. 28: Waterfall diagram for the longitudinal vibration of the radar mast Example 2 The first voyages after commissioning of a container ship led to damage of deckhouse equipment. and equipment parts in the engine room. and excerpts from these curves are given in Fig. e. However. crane boom. 28. agreed to perform an investigation of the vibration behaviour for two sea conditions: one in a sea area as calm as possible. The frequencies of 1. but by the seaway.g. Fig. 29 shows measured amplitude spectra of deckhouse vibrations in the longitudinal direction in calm as well as in rough seas. a complete balancing of the 2nd order free mass moment was achieved. the other in rough waters. radar mast. The mast vibrations were greatly reduced by increasing the natural frequency to about 11 Hz. therefore.60 Hz can be assigned to global hull vibrations. Fig. longitudinal direction 41 .The natural frequency of the radar mast at 9 Hz exhibited proximity of resonance to the propeller blade frequency at almost full engine speed (9. Detuning of the natural frequency was achievable only by difficult-to-implement reinforcements of the mast foundation or by means of bracings or stays extending. the amplitudes shown were not excited by the propeller or engine. Considerable slamming impacts occurred in the forward part of the ship. It was not expected that further stiffening of the mast structure itself would produce any significant effect. 30.
The investigation underlined that severe slamming impacts extending over a long period of time must definitely be avoided. definite structural deficiencies were also found in the detailed design. three slamming impacts Fig. This resulted in slamming impacts.Fig. 30: Rough sea. measurements covered the investigation of the vibration behaviour of the entire deckhouse as well as of its possibly inadequate incorporation in the hull structure. both for the comfort of the crew and for the integrity of the structure. it was found that the damage was caused by operating the vessel almost non-stop in bad weather during the first few voyages at shallow forward draught. However. Example 3 The starting point for these measurement-related investigations consisted of cracks that occurred on the main deck at the aft edge of the deckhouse just shortly after commissioning of the ship. 31: Excerpts of above time signals As a conclusion of the investigation. In addition. machinery and electronic equipment (radar mast). which occurred more frequently and even more severely than measured. 42 . The ship operator was concerned that vibrations in this area were the cause of the damage and that other areas of the structure might similarly be found to be damaged later on. the vibration behaviour caused by the propulsion plant was satisfactory. Therefore.
This isolated vibration behaviour of the deckhouse is unusual. 32. The seaway is the only possible source of excitation. the aft bulkhead of the deckhouse. exciting the 2. and thus the detected cracks. which in turn act as a source of excitation at the footing of the deckhouse.	np : 160-204 r/min •	Reversal	from	full	speed	ahead	to	full	speed	astern •	nchor-dropping	manoeuvre.and 3-node vertical hull vibrations of the ship. Evaluation of the speed-up manoeuvre led to a surprising aspect that can be seen in Fig. Amplitudes remained almost constant over the entire speed range. Manoeuvre 2 makes it possible to determine resonance points and to estimate associated amplitudes.	propulsion	plant	not	operating A Manoeuvre 1 gives the vibration level at nominal speed and thus presents the main part of the vibration concerning fatigue strength of welded joints in question. were situated close to the aft node of the vertical 2-node vibration mode and were. briefly rising only in case of resonance with the propeller blade frequency.Signals from 14 accelerometers distributed over the main deck and the deckhouse region were recorded simultaneously for each of the following manoeuvres: •	Nominal	speed. Evaluation of measurement results revealed the following overall picture: Amplitudes at various rigid points of the ship were small and gave no cause for complaint. The deckhouse turned out to vibrate completely isolated from the hull at a frequency of 10 Hz. Manoeuvres 3 and 4 were intended. in the unfavourable region of high alternating stresses. However. 32: Waterfall diagram for the longitudinal acceleration on the bridge deck 43 .	np : 204 r/min •	Run-up	of	main	engine. showing the longitudinal vibration of the deckhouse. therefore. to reveal lower natural frequencies of the ship’s hull and corresponding vibration modes with regard to the possibility of inadequate mounting of the deckhouse. in particular. Fig.
Fig. to raise the relevant natural frequency of the deck-house to a value above that of the 4th-order excitation at nominal speed.	B	and	C)	(Additionally. For variant C. •	Initial	situation	•	Schneekluth	nozzle	•	Connection	of	funnel	to	deckhouse	(incl.) Variant	A Variant	B	Variant	C Variant	D The main cause of the high vibration level was the excitation of the 4th order. 33: Waterfall diagram for the longitudinal acceleration of the bridge deck Example 4 The first unit of a series of container ships exhibited an unsatisfactorily high level of longitudinal vibration of the deckhouse in the vicinity of nominal propeller speed (100 r/min). therefore. Due to this. So as not to jeopardise the success of this ship type by an unfavourable impression of its vibration behaviour. the natural frequency has fallen again. Fig. the initial situation was somewhat improved. Important orders and significant amplitude changes as a function of revolution rate are recognisable. 34: Order analysis of the propeller blade frequency In the speed range up to 100 r/min. variant D shows a further reduction in the vibration level. namely. the propeller blade frequency. these points should be examined for new cracks after every period of rough weather. Corresponding deficiencies of production did not occur on the sister ships.e. after completion of repairs. 34 as an order analysis for the propeller blade frequency. The amplitude reduction below speeds of 100 r/min is due to the damping tank. 33 shows the waterfall diagram of a speed-up manoeuvre for longitudinal vibrations at the top of the deckhouse. In reconstructing the manufacturing process (mounting of the deckhouse on the main deck). the shipyard decided to per-form experimental investigations for three different variants. Comparison of the four variants concerning longitudinal vibration of the deckhouse is shown in Fig. variant D differed from other variants in that its deckhouse was 2 m taller. As a result of the increased height of the deckhouse. namely. vicinity of resonance) up to 103 r/min. Fig.	B)	•	Damping	tank	(incl. stiffness effect of the funnel connection was compensated to a certain degree. It was. recommended that. was achieved. both of a hydrodynamic and of a structural nature.This vibration behaviour supported the presumption of comparatively poor vertical connection of the deckhouse. whereas the steep rise for this variant is attributable to the taller deckhouse. Through use of the Schneekluth nozzle (variant B). The aim of the funnel connec-tion. These had to be regarded as having contributed to the cracks. 44 . No further cases of relevant vibration damage came to light. various deficiencies and inaccurate fits were found in the region of the aft bulkhead of the deckhouse. leading to significant amplitudes in rough seas. but above that speed there is again a steep rise (i.
it had to be demonstrated experimentally that there was no danger of resonance between a fundamental vibration mode of the frame and the ignition frequency of 25 Hz. 35). the diesel generator unit and the base-frame were investigated with the aid of appropriate theoretical analyses. it must be ensured beforehand that the exciter’s range of force and frequency is appropriate for the vibration question concerned. it turned out to be advantageous for these measurements to exceed the nominal speed range as far as possible. recommendations for the final design were ultimately obtained. mechanical unbalance exciters are particularly suitable. Generator set Exciter Exciter Horizontal excitation forces Vertical excitation forces Fig. since they generate a defined harmonic force. Naturally. 35: Arrangement of the exciter 45 . Because vertical and horizontal vibration modes were important here. In a first step. the exciter unit was mounted in such a way that both horizontal and vertical forces acted on the base-frame at points above the elastic mounting (Fig. this excitation force – which increases quadratically with the revolution rate – can be varied within certain limits. Example 5 For a diesel generator unit installed on an elastically mounted baseframe. by the use of different masses.The investigation firstly underlined that extensive measurements above the standard scope – possibly in conjunction with theoretical analyses (FE computations) – can contribute significantly towards optimisation of the vibration behaviour. Furthermore. By means of various calculations in which the structure was varied. so that a relevant danger of resonance could be detected in this range. For this kind of experimental investigation. Secondly.
The main results are summarised in the following Table 5: Table 5 Natural frequency [Hz] 10. The following operating conditions were investigated during the second sea trial: •	Speed-up	•	Constant	speed	•	Constant	speed	•	Constant	speed	n	=	130	to	174	r/min.4 12.8 41. which was performed in steps of 5 rpm. propellers. Of crucial importance was the question how the ship’s vibration behaviour would change as a result of the greater draught during the second sea trial. vertical Frame. signals of seven accelerometers and a load cell between the exciter and the frame structure were recorded simultaneously. the result of the modal analysis of the vertical frame bending mode is shown in Fig. torsion Natural frequencies of the rigid body modes were only of secondary interest here. shaft bossings. 36: Modal analysis 46 . no danger of resonance with the ignition frequency of the engine (25 Hz). parallel measurements of shaft power and mechanical vibrations at various locations were performed to obtain a comprehensive picture of cause and effect. the measuring direction of the accelerometers corresponded to the force direction of the exciter. but also for plane structures such as panels. extensive measurements were performed during a second sea trial. propeller nozzles.	propeller pitch 100% n	=	174	r/min. turbochargers and so on. Frequencies below 10 Hz could not be generated by the exciter.In each case. During each measurement.2 There was. In all cases. The results determined theoretically were thus confirmed. vertical bending Frame.1 31. consequently.	propeller	pitch	10-100% n	=	174	r/min.5 46.	propeller	pitch	100% n	=	174	r/min. for example subsystems such as rudders. Vertical bending The waterfall diagram of pressure pulses (Fig. The disadvantage is the comparatively large effort needed for mounting the exciter on the structure involved and the exciter’s limited range of force and frequency. horizontal bending Frame. Fig. To investigate the behaviour of the propeller. The procedure for determining natural frequencies by means of a mechanical unbalance exciter is basically suitable for a large number of elastic systems. about the transverse axis Rigid body. Greater draughts often reduce the vibration level. about the longitudinal axis Rigid body. 37) shows the dominance of the propeller blade frequency during the speed-up process. while the exciter was slowly passing through the frequency range from about 10 Hz to 50 Hz. Example 6 Strong vibrations in the aft part and in the deckhouse of a small container ship came to light during a first sea trial and were attributable to the propeller as source of excitation. 1st sea trial) Vibration mode Rigid body.	propeller	pitch	70-100%	(with lower draught.5 13. coherence and transfer functions of the load cell as well as of one significant acceleration signal were checked with the aid of a frequency analyser to monitor the statistical dependence of the two signals. and the shipping company can often accept the worse behaviour at ballast draught in case this condition plays no significant role in the future lifetime. In addition to pressure pulses acting on the ship’s shell in the vicinity of the propeller. 36. As an example. including the magnitude of pressure fluctuations.
700 kW power.000 kW from a strength point of view. 47 . P2 and P3 as a function of power exhibit a steeper rise from about 4. 38). Amplitudes increase from values which are already high (10 kPa). Fig. upwards (Fig. 37: Waterfall diagram of the propeller pressure fluctuations Pressure pulses of three measurement points P1.500 kW was used as basis for the hydrodynamic design. In this case. 39). by almost 40% to 14 kPa for the lower draught investigated (Fig. an acceptable vibration level was achieved by a new propeller. However. 38: Pressure fluctuations as a function of power The effect of the draught on pressure pulses at propeller blade frequency is pronounced. 39: Pressure fluctuations of P1 for the two draughts This example shows the great extent to which pressure fluctuations depend on the design point and how a ship’s vibration level can be influenced by an inadequate propeller design. [kPa] 14 12 10 8 6 4 2 0 0 1000 2000 3000 4000 5000 [r/min] 180 170 160 150 140 130 120 6000 Shaft power [kW] Fig. or 160 rpm.Fig. Discussions about the propeller design revealed in retrospect that the propeller was adequately designed for the power of 6. a reduced power of 4.
for inspectors of shipping companies. in particular. The procedures outlined can be applied to treat vibration questions on a rational basis at the design stage. such as the “International Ship & Offshore Structures Congress”. including the FE models. The paper documents the “state of the art” in the field of ship vibration technology. although this list does not claim to be complete. Conclusions The foregoing remarks show how questions regarding ship vibrations can be dealt with comprehensively from a contractual. theoretical and experimental point of view. such as •	torsional	vibrations	of	shafting	systems •	elastic	mounting	of	engines	and	equipment	items	•	sloshing •	slamming	(whipping	and	springing) •	shock are beyond the scope of this document. in engineering offices. It is intended to be used as a manual in the daily work at shipyards. The subjects dealt with certainly do not cover the entire field of vibration technology. By presenting a wide range of knowledge in this field. the paper contributes to prevent vibration problems on newbuildings as well as to find the most cost-effective solutions for vibration problems occurring on ships already in service from a well-planned measurement action. also be used to solve vibration problems on ships already in service. Details of these subjects may be found in the literature mentioned.6. It is recommended that interested parties keep themselves informed of international activities. furthermore. 48 . They can. we thank all those shipyards and shipping companies that kindly gave us permission to present some results. The treatment of further topics. Finally. ISSC. and so on.
Journal of Scientific Computing. Edition 1997. Chapter 16 . Vol. SIAM.:	“Elastic Ship Hull Girder Vibrations in Restricted Water” (in German). Report No.	P.7.: “The Inertia of the Water Surrounding a Vibrating Ship”. F. R öhr. reporting and evaluation of vibration with regard to habitability on passenger and merchant ships”. Institut für Schiffbau.: “Numerical Analysis of Hydroelastic Problems using the Singularity FE method” (in German). Jahrbuch der STG. Edition 1989. SNAME Transactions. P.: “Ship Vibrations under Consideration of Gas Pressure Forces Induced by Slow-Running Two-Stroke Engines” (in German). 91.Machinery Installations”. International Standard ISO 6954: “Mechanical vibration – Guidelines for the measurement.: “Error Bounds for Dynamic Responses in Forced Vibration Problems”.	Möller. Part 1 . H. Part 1: Part 2: Part 3: Part 4: [7] General guidelines Large land-based steam turbine generator sets Coupled industrial machines Gas turbine sets Part 3: Part 4: Part 6: Industrial machines with nominal power above 15 kW and nominal operating speeds between 120 r/min and 15000 r/min when measured in situ Gas turbine driven sets excluding aircraft derivatives Reciprocating machines with power ratings above 100 kW [2] [8] [3] Germanischer Lloyd: “Rules for Classification and Construction.Ship Technology. Simon. I .Seagoing Ships. Vol. 42. Lewis. International Standard ISO 2631-1: “Mechanical vibration and shock – Evaluation of human exposure to whole-body vibration. M. Edition 2000. Edition 1984. Jahrbuch der STG. Computing. Germanischer Lloyd: “Rules for Classification and Construction. Asmussen.. 91. Part 1 . 37. Asmussen. Edition 1996.: 49 . 1929. Payer. Passenger Ships (v ≤ 25 kn)”. Part 1: Part 2: General guidelines Large land-based steam turbine generator sets in excess of 50 MW [15] [16] Asmussen. I . Part 2: Continuous and shock induced vibration in buildings (1-80 Hz)”. Hamburg. 1980. 1994. Part 1: General requirements”.	U. I.. Math.Seagoing Ships. Edition 2000. G.: “Vibration Response on Propulsion-Efficient Container Vessels”. Mumm. SNAME Transactions. Literature [1] International Standard ISO 6954: “Mechanical vibration and shock – Guidelines for the overall evaluation of vibration in merchant ships”. 1985. 1984.: “The Lanczos Algorithm with Partial Reorthogonalisation”. H.Ship Technology. Edition 1996. [9] [4] [10] [5] [11] [12]	[6] [13] [14] International Standard ISO 10816: “Mechanical vibration – Evaluation of machine vibration by measurements on non-rotating parts”. A. I. Kaleff. C. I. 93. 1997. 15. H. Edition 2001 International Standard ISO 7919: “Mechanical vibration of non-reciprocating machines – Measurements on rotating shafts and evaluation criteria”. Vol.Rules on Rating Noise and Vibration for Comfort. Vol..Harmony Class .. 1991. Cabos. Chapter 2 . 401. Vol. International Standard ISO 2631-2: “Mechanical vibration and shock – Evaluation of human exposure to whole-body vibration. Vol. Müller-Schmerl.
H. Wageningen. O.: ”Damping in Propeller-Generated Ship Vibrations”.: “Methods for Vibration Analysis” (in German). XIII. 1974. Nath. 1979. I. Report No MB 81-80 (in German).: [18] [20] [30] [21] [31] [22] [32] [23] [33] [24] [34] [25] [35] [26] [36] [27] 50 . Kerwin. Streckwall.: “Early Design Stage Approach to Reducing Hull Surface Forces Due to Propeller Cavitation”. 5th Duisburger Colloquium for Ship and Offshore Structures. FDS-Report No. Willich. Yamaguchi. Vol.	Issue	2/3. Hoshino. Issue 12. S. 1988. Björheden.“Consideration of Medium-Speed Four-Stroke Engines in the Assessment of Ship Vibrations” (in German).. 468. K. Clough. E. 1994. 83. London. S. 1977. Conf. T. T. PhD Thesis RWTH-Aachen. al: ”Development of Marine Propellers with Better Cavitation Performance”. C. 1976. Asmussen. Proceedings of Int. Chao. Pedersen. 2. HANSA. Spring Meeting of the Society of Naval Architects of Japan. K.: “A Contribution for the Determination of Damping in Ship Vibrations” (in German).. 1980. I. al: “Introduction of Main Engine Excitation into the Ship Structure” (in German). Schiff und Hafen. K.: “Some Aspects to the Propeller-Bearing Forces Exciting Hull Vibration of a Single Screw Ship”.: “Simulation of Low-Speed Main Engine Excitation Forces in Global Vibration Analyses”.10. Holden. PRADS Proceedings Vol. Bathe. Lee. 257. G. STG-Expert Panel on Ship Vibrations. 1986. H. Raestad. Hylarides. S. Vol.	University	of	Alabama. et. T. E. 1961. D. W.: “The Cavitating Tip Vortex of a Propeller and the Resulting Pressure Fluctuations” (in German). Handbuch der Werften. Jahrbuch der STG. 86. 1981. Report No.: “The Relative Importance of Ship Vibration Excitation Forces”. Köster. 1988.	Vol. 1989. 24.: “Prediction	of	Steady	and	Unsteady	Marine	Propeller	Performance by Numerical Lifting-Surface Theory”. H.	Huntsville. 88. K.	UAH	Press	1972.: “Local Vibrations On-board Ships” (in German).. Asmussen.: “Finite Element Analysis of Dynamic Response”. R. 1995. E. A. H. 3rd Report. D. Issue 13. Frostad. C. 99. [17] Jakobsen. Advances in Computational Methods in Structural Mechanics and	Design.: “Computation	of	the	Propeller	Flow	Using	a Vortex-Lattice Method” (in German). Wissenschaftliche	Zeitschrift	der	Universität	Rostock. Vol.: ”Coupled Axial and Torsional Vibration Calculations of Long-Stroke Diesel Engines“. NSMB. Vol. 1987 Wedel-Heinen. Hamburg..: “Vibration Analyses in Practice” (in German). [29] [19] Lehmann. A.. et.: “Vibration Analysis of Imperfect Marine Structural Elements”. BMFF-MTK 440 D.. T. G. J. Schiffstechnik Vol. 1989. London. RINA Symposium on Propeller-Induced Ship Vibration. Fagerjord. Skaar. Weitendorf. R. 1978. Vol. Y. on Noise and Vibration in the Marine Environment.: “Highly-Skewed Controllable Pitch Propellers”. Mumm. SNAME Transactions... 1991. SNAME Transactions. O.. SNAME Transactions. Publ. 118. B. E. Matthies. RINA.. [28] Kumai. J. Vol. No. 1991.
Hamburg Germanischer Lloyd Press & Public Relations. Streckwall. Vol. Hamburg Nissen | Carstensen Communication Consulting GmbH PR Office.: “Quantities of Propeller Excitation as a Function of Skew and Cavitation for Performing Vibration Analyses” (in German). M. G.O. Jahrbuch der STG. Box 11 16 06. [38] [39] [40] Published by Edited by Layout by Germanischer Lloyd Aktiengesellschaft. Hamburg Eugen Klaussner. Germanischer Lloyd. 1985. 1991. 1995. Hamburg Kirsten Siedenburg-Evers. H. 228. Norton: “Fundamentals of Noise and Vibration Analysis for Engineers”. Germany The contents may be reproduced free of charge on condition that an acknowledgement is sent to Germanischer Lloyd. FDS-Report No.	ISBN 0 521 34941 9. Translations by Publishing house Printed by . 20416 Hamburg.“Application	of	Quasi-Continuous	Method	to	Unsteady	Propeller Lifting Surface Problems”. Germany P. Mumm. Journal of the Society of Naval Arch. 158.	Cambridge	University	Press.: “Comparison of Two Methods for Computation of Propeller Induced Pressure Oscillations” (in German). I. H. 22453 Hamburg. Germany Phone: +49 40 36149-0 Fax: +49 40 36149-200 headoffice@gl-group. Vieweg ISBN 3-528-18145-1.. 89. kse-design.com Print Media Innovation. Natke: “Introduction to Theory and Practice of Time Series and Modal Analysis” (in German). Ritterhude Selbstverlag des Germanischen Lloyd Vorsetzen 35. 20459 Hamburg. [37] Asmussen. Vol. H. P. of Japan.
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