bluuebunny/crossref_metadata_2025 huggingface dataset:
Numerical Calculation of the Wave Integrals in the Linearized Theory of Water Waves
Authors: Shen Hung-Tao , Farell Cesar
Published: January 2021

A method for the numerical evaluation of the derivatives of the linearized velocity potential for three-dimensional flow past a unit source submerged in a uniform stream is presented together with a discussion of existing techniques. It is shown in particular that calculation of the double integral term in these functions can be efficiently accomplished in terms of a single integral with the integrand expressed in terms of the complex exponential integral, for which numerical computing techniques are available.
Optimal Shape of a Planing Surface at High Froude Number
Authors: Ting Lu , Keller Joseph B.
Published: January 2021

A planing surface moving at high Froude number throws up a jet that is responsible for the leading term in the drag. By shaping the surface appropriately, the jet can be eliminated. The drag is thereby reduced by a factor of order (Fr)–2. The paper shows how this can be done for a two-dimensional planing surface consisting of two flat plates. It is found that the lengths of the plates must have a ratio dependent upon their angles of inclination. Then the angles that maximize the lift coefficient are determined.
Aerodynamic Model Study of Marine Gas Turbine Exhaust Cooling
Authors: Marquand C. J.
Published: January 2021

Problems such as the overheating of aerials by hot exhaust gas have been experienced by the Royal Navy on their new generation of gas turbine powered ships. Model tests indicate that the temperature trajectories from square, rectangular and clusters of circular exhausts may be correlated on the same basis as single circular exhausts, by substitution of a characteristic dimension in a simple temperature-decay equation. Plume temperature measurements show that lower temperatures can be obtained by enhancing the vortex activity in the plume, thereby causing more ambient air to be entrained, and that this can be achieved by using exhausts other than circular, where the plume drag is increased. Plume temperatures may also be reduced by introducing air entrainment into the uptake itself. Here it is important to ensure that the low-momentum entrained cooling air surrounds the hot exhaust jet as it leaves the uptake. It is then easily deflected into twin vortices in the downstream plume and these entrain ambient air. Air-entraining exhausts produce at least 20 percent lower % CTmax values in the downstream hot gas plume than more conventional exhausts.
A Note on the Form of Ship Roll Damping
Authors: Dalzell J. F.
Published: January 2021

The objective of the present work was to develop an approximation to the conventional mixed linear-plusquadraticship roll damping model so that analytical obstacles could be overcome in the application of the functional series expansion to nonlinear ship rolling. A mixed linear-plus-cubic approximation was found to be reasonable for this purpose. In the course of analyses, there were indications that this model may be closer to an "equivalent approach" than to an "approximation."
A Localized Finite-Element Method for Two-Dimensional Steady Potential Flows with a Free Surface
Authors: Bai Kwang June
Published: January 2021

A numerical method is presented for solving two-dimensional uniform flow problems with a linearized free-surface boundary condition. The boundary-value problem governed by Laplace's equation is replaced by a weak formulation (also known as Galerkin's method) with certain essential boundary conditions. The infinite domain of the fluid is reduced to a finite domain by utilizing known solution spaces in certain subdomains. The bases for the trial and test functions are chosen from the same subspace of the polynomial function space in the reduced subdomain. The essential boundary conditions are properly taken into account by an unconventional choice of the basis for the trial functions, which is different from that for the test functions in other subdomains. This method is applied to two-dimensional steady flow past a submerged elliptic section, a hydrofoil at an arbitrary angle of attack, and a bump on the bottom. In each example the body boundary condition is satisfied exactly. Both subcritical and supercritical flows are treated. We present the numerical results of wave resistance, lift force, moment, circulation strength, and flow blockage parameter. The computed pressure distributions on the hydrofoil and wave profiles are shown. The test results obtained by the present method agree very well with existing results. The main advantage of this method is that any complex geometry of the boundary can be easily accommodated.
Comments on Second-Order Wave Effects on Large-Diameter Vertical Cylinder
Authors: Chakrabarti Subrata K.
Published: January 2021

In a recent paper, Raman et al (RJV) [1] 2 presented a second- order solution for the wave interaction with a large-diameter, bottom-mounted, surface-piercing, fixed vertical cylinder. Earlier, Chakrabarti [2,3] obtained an approximate solution for the vertical cylinder due to Stokes's fifth-order wave. Later, Yamaguchi and Tsuchiya (YT) [4] proposed a second-order solution in a closed form for the wave interaction problem with the vertical cylinder which was examined by Chakrabarti [5]. All these solutions are different due to the assumptions regarding the frequency of the scattered wave and the kinematic free-surface boundary condition. RJV [1] claim that their solution is superior to the earlier solutions because, according to them, it satisfies the nonlinear free-surface boundary conditions completely.
Evaluation Study of A Three-Speed Hydrofoil with Wetted Upper Side
Authors: Rowe Alain
Published: January 2021

A supercavitating foil with a rounded leading edge and wetted upper side is presented. The characteristics of this foil are forecast in view of its being used on a three-speed hydrofoil craft. The real foil, whose angle of sweepback is left undefined, is simulated by a model of rectangular planform with aspect ratio two. Tests in a tunnel with a free surface show that a higher efficiency is obtained with this model than with a supercavitating foil with nonwetted upper side. Comparison with previous results related to a cambered parabolic foil demonstrates a much wider range of stability at top speed. The improvement is probably due to the use of a light, well-distributed specific load. The importance of this improvement, however, poses acutely the problem of the similarity concerning the area of stability.
On the Optimum Wageningen B-Series Propeller Problem with Cavitation-Limiting Restraint
Authors: Markussen P. A.
Published: January 2021

For the most widely encountered preliminary propeller design problem, in which absorbed power and speed of revolutions are given and the speed of advance estimated, three simultaneous equations are derived from which, using the Wageningen B-Series polynomial coefficients for propeller thrust and torque coefficients with Reynolds number corrections, the optimum blade area ratio, pitch ratio, and advance coefficient can be solved mathematically by means of an iterative procedure on a digital computer. With these variables known, the propeller particulars, thrust and torque coefficients, optimum efficiency, and open-water and cavitation characteristics can easily be calculated.
On the Maximum Deflection of Plating in Newly Built Ships
Authors: Antoniou A. C.
Published: January 2021

Various efforts have been made in the past to express the central deflection of the plate panel as a function of the basic parameters, such as plate slenderness, welding thickness, etc., upon which it depends. Distortion tolerances of the plate could thus be specified as a function of the central deflection, which is easily established. The present paper analyzes more than 2000 measurements of plate panel central deflection in newly built ships collected over a number of years in a shipyard. The central deflection is expressed as a function of the plate slenderness ratio, the thickness of the stiffeners, the plate aspect ratio, and the weld throat thickness. A regression analysis is carried out to determine the coefficients of the functional relationship. From the regression analysis the influence of each parameter on the deflection is derived and new formulas for predicting maximum deflection in various cases are proposed. Finally, results of the analysis with various parameters included are compared with similar formulations previously given in the literature, and a new formula for specification of post-welding distortions is suggested.
Strip Theory of Ship Motions in the Presence of a Current
Authors: Triantafyllou Michael S.
Published: January 2021

The strip theory is reformulated to account for the presence of a current with longitudinal and side components. The roll, sway, and yaw motions are coupled in this case with pitch and heave. Results supported by experiments show a strong influence on roll near resonance.
A Modified Displacement-Body Method for Treating the Axisymmetric Strong-Interaction Problem
Authors: Hoffman Gilbert H.
Published: January 2021

A modification of the displacement-body method is presented for calculating the high-Reynolds-number, strong-interaction flow field in the aft region of a body of revolution. The modification is based on a simple pressure mapping which effectively represents streamline curvature effects in the vicinity of the tail. The mapping is derived and the method applied to three representative axisymmetric bodies for which experimental data are available. The boundary-layer equations and potential flow equations are solved by a standard finite-difference and surface singularity method, respectively. Calculated results for the body pressure distribution, momentum deficit area, and body drag are found to agree well with experiment.
A Zone-Interaction Method for the Outer Flow Analysis of a Separated Airfoil
Authors: White James W.
Published: January 2021

The pressure distribution over a subsonic airfoil experiencing massive separation is analyzed by a zonal modeling approach. Important physics are included in the mathematical description of each zone, and the zones are allowed to interact until convergence of the overall flow is obtained. The separated region is modeled as a zone of uniform pressure, the magnitude of which is determined by the solution method. The elliptic effect of the separated flow on the pressure field over the airfoil is included by bounding the stalled zone by two free streamlines which are iteratively located. Influence of the wake on the airfoil flow is modeled by two parallel strips which allow the subambient pressure in the stalled zone to adjust continuously black to freestream conditions. A Cauchy principal-value integral equation is used to compute the potential flow with no restrictions on the airfoil contour. Unlike most complex-variable methods, no mappings are required and the numerical solution is obtained entirely in the physical (Z) plane.
The Tearing Strength of Mild Steel Plate
Authors: Vaughan H.
Published: January 2021

The penetration of a thin plate from the side by a sharp rigid wedge is considered. A formula is proposed which expresses the external work done in terms of the depth of penetration and the wedge angle. The external work is decomposed into two parts: a part related to the length of cut plate and a part related to the amount of plastically deformed material. This decomposition introduces two material coefficients and two exponents which describe the dependence of each energy function on the plate thickness. The results of 70 impact tests are presented which verify the validity of the proposed formula and which have also been used to determine the aforementioned material constants and exponents for mild steel.
Diffraction of Waves Around a Ship
Authors: Liapis Nikolas , Faltinsen Odd M.
Published: January 2021

The diffraction problem of a fixed slender ship in incident regular sinusoidal deep-sea waves coming from any direction is formulated. The waves are assumed to be of the same order of magnitude as the beam of the ship. Zero Froude number is assumed. The boundary-value problem is linearized with respect to the wave amplitude and solved by the method of matched asymptotic expansions. A solution valid for all wave headings is found. The solution involves solving a two-dimensional Helmholtz equation problem for cross sections along the ship. The Helmholtz equation problem is solved by a new fast integral representation method. Numerical solution procedures are given. The pressure distribution for different wave headings and wave lengths is calculated and compared with experiments. The agreement between theory and experiments is found to be satisfactory.
Wave Power Extraction from a Transient Heaving Cylinder
Authors: Hudspeth Robert T. , Siotta Larry S.
Published: January 2021

Wave power extracted from the transient motion of a periodically restrained-released heaving circular cylinder proposed by Falnes and Budal is examined under the limitations of linear wave theory excitation. Numerical estimates for the normalized radiated wave amplitudes required for the wave force excitation derived by Mei are computed from the computationally efficient variational method developed by Black and Mei for the wave force diffraction regime. Wave power estimates for the rising period only of the heaving motion are given, while the falling period of the motion is neglected. A graphical summary is presented which demonstrates the parametric dependency of the dimensionless wave power rate on the design wave parameters and the body geometry for three general types of transient power systems heaving in deepwater conditions. The total power requirements for the complete power extraction system as well as the real fluid viscous effects are not included.
Optimal Ship Forms for Minimum Wave Resistance
Authors: Hsiung Chi-Chao
Published: January 2021

By introducing a set of "tent" functions to approximate the ship hull function, the Michell integral for wave resistance is reduced to a standard quadratic form in terms of ship offsets. With linear-inequality constraints of the type 0 ≤ H(x, z) ≤ B;C ≤ Hx(x,z) ≤ D(where H(x,z) is the hull function and B, C, D are constants), we are able to find various optimal ship forms of minimum wave resistance by applying quadratic programming techniques to the problem. Three optimal forms have been chosen among a number of computed results for tests in the ship-model towing tank. All three models have afterbodies identical with that of Series 60, Block 60, a standard merchant ship hull of good quality. Although the experimentally determined residuary resistance is in no better agreement with the theoretically predicted results than is usual in such comparisons, the order of "goodness" of the hull-forms as predicted and as measured was the same for Fn ≥ 0.36 and also for 0.20 ≤ Fn ≤ 0.26.
Some Experimental Results with Ship Model Acceleration Waves
Authors: Çalisal S. M.
Published: January 2021

The wave resistance of a ship moving at a constant speed can be calculated using information obtained from its wave pattern. One of the basic assumptions in wave survey methods is t1he existence of a time-independent model speed. In towing tanks initial acceleration is unavoidable. Wehausen (1964) showed that the effect of initial acceleration on wave resistance has a decaying and oscillating character. Çalişal (1977) gave the general form of the initial acceleration potential and showed the existence of a two-dimensional wave of the formζT=AcTsin[14k0(x−cT)+ϕ(t)]+0(cT)−2(1)To study the validity of the theoretical results, some experiments were performed. The variation of the measured spectra and the frequencies within the recorded total resistance pitching moment are of interest. Results indicate that models should travel a distance proportional to the square of the Froude number before wave data collection can begin, that the predicted encounter frequency exists in the recorded total resistance and pitching moment signals, and that special effort is required to avoid initial acceleration waves due to wall effects.
Wing Sections for Hydrofoils—Part 2: Nonsymmetrical Profiles
Authors: Shen Young T. , Eppler Richard
Published: January 2021

Based on wing section design theory and boundary-layer calculations, a series of symmetrical hydrofoil sections with improved hydrodynamic characteristics in terms of cavitation inception was successfully developed and presented in a previous paper. The design method is applied to develop a series of nonsymmetrical hydrofoil sections having a minimum pressure bucket whose depth and width are adapted to practical applications. Its depth, namely, the bottom value of — Cpmin, is made as low as necessary to achieve a certain critical cavitation speed; its width is made as large as possible to tolerate fluctuations of large angles of attack. Hydrodynamic properties of these newly developed hydrofoil sections are compared with those of NACA 16 and NACA 66 (MOD). The ability to achieve significant delay in cavitation inception makes the present design method useful when applying it to hydrofoils as well as to marine propellers.
TVC Noise Envelope—An Approach to Tip Vortex Cavitation Noise Scaling
Authors: Latorre Robert
Published: January 2021

Noise measurements of the tip vortex cavitation generated by a large model hydrofoil and its one-quarter scale model are presented to discuss the features of tip vortex cavitation (TVC) noise and noise scaling. The concept of the TVC noise envelope is introduced to divide the cavitation noise into incipient and fully developed TVC noise. The cavitation noise scaling method of Bojorheden and Astrom is compared with the method of Levkovskii for scaling the fully developed TVC noise. A theoretical model of the cavitation nuclei spiraling around an idealized Rankine vortex is introduced to model the characteristic bursts in the incipient TVC noise and predict the inception of TVC noise. The simulation results for the large and small foils are shown to be in good agreement with the experimental noise measurements.
Design Charts for Self-Excited Whirling Critical Speeds
Authors: Yagoda H. P. , Ketchman J
Published: January 2021

Employing a generalized tailshaft model of the propulsion system, design charts are constructed for rapidly estimating self-excited whirling critical speeds of the shafting system over a wide range of design parameters. These design chart estimates may be refined to any desired accuracy by a program developed for a programmable hand calculator. The analysis includes propeller mass and rotatory inertia, propeller gyroscopic effects, shaft mass and flexural rigidity, and partial fixity of the line shafting at the forward bearing. Entrained water may be included as a proportion of the propeller mass and inertia. The nondimensional form of the design charts offers several advantages, for example, the option of employing any consistent system of units, or to quickly assess the sensitivity of the critical whirling speeds to design parameters of the system. Comparison of results with other methods is very favorable.
A Nonlinear Method for Predicting Unsteady Sheet Cavitation on Marine Propellers
Authors: Stern Frederick , Vorus William S.
Published: January 2021

A method is presented which provides a basis for predicting the nonlinear dynamic behavior of unsteady propeller sheet cavitation. The method separates the fluid velocity potential boundary-value problem into two parts, static and dynamic, which are solved sequentially in a forward time stepping procedure. The static potential problem is for the cavity fixed instantaneously relative to the propeller and the propeller translating through the nonuniform wake field. This problem can be solved by standard methods. The dynamic potential represents the instantaneous reaction of the cavity to the static potential field and thus predicts the cavity's deformation and motion relative to the blade. A solution is obtained for the dynamic potential by using the concepts of slender-body theory to define near-and far-field potentials which are matched to form the complete solution. In the far field, the cavity is represented by a three-dimensional spanwise line distribution of sources. In the near field, the cavity is approximated at each cross section as a semi-ellipse with unknown axes a(t), b(t), and position l(t) along the chord of the foil section. Conditions are derived that determine (a, b, l) by minimizing the square error in satisfying the dynamic boundary condition. These conditions yield the equations of motion of the cavity in the form of three coupled nonlinear second-order ordinary differential equations with time as the independent variable. The theory is presented for the general foil and not specifically for propellers. However, the method incorporates features in its formulation which facilitate its application to marine propellers. The method is demonstrated by using the steady noncavitating potential for the two-dimensional half-body as an approximation to the static potential. Both fixed and unsteady cavities are calculated. The unsteady cavities are calculated by varying the hydrostatic pressure in the half-body pressure field sinusoidally.
A Hydroelastic Approach to Ship Vibration Problems
Authors: Kaleff Peter
Published: January 2021

A procedure is presented to determine the vibration frequencies and mode shapes of submerged structures. Hamilton's principle is used to formulate the problem, and general sequences of trial functions are introduced to permit the direct extremization of the corresponding energy functional. The fluid-structure interaction is accounted for by restricting the trial functions of the fluid to represent the flow around the immersed body imposed by each trial function of the structure. The trial functions for the fluid are built up from the contributions of triangular constant source elements distributed over the wetted surface of the structure, the accuracy of which in representing a flow is tested on an accelerated sphere. The structure is modeled with finite elements. The accuracy of the hydroelastic procedure is accessed on two examples as compared to experimental data: a cantilever plate and a freely floating ship.
The Creep Behavior of a Floating Beam
Authors: Xirouchakis Paul C.
Published: January 2021

The creep response is obtained for an inhomogeneous beam, with simple end supports, resting on a liquid foundation and subjected to a sinusoidally distributed load. The Norton-Bailey constitutive equations are used to describe secondary creep behavior and elastic effects are retained. The liquid foundation is taken as a continuous Winkler support. The beam cross section is replaced by a double-membrane model. The implications are discussed of using stress or deflection failure criteria in determining the magnitude of the instantaneous breakthrough load. The linear viscoelastic as well as nonlinear creep beam response is obtained explicitly. The influence of the beam geometric and material characteristics and of the presence of the liquid foundation on the growth of the deflections with time is discussed. The variation of the breakthrough load with failure time is also explored. Results obtained are compared with available sea ice laboratory test data.
On Wall Effects in Cavity Flows
Authors: Hsu C. C.
Published: January 2021

Simple wall correction rules for two-dimensional and nearly two-dimensional cavity flows in closed or free jet water tunnels, based on existing linearized analyses, are made. Numerical results calculated from these expressions are compared with existing experimental findings. The present theoretical predictions are, in general, in good agreement with data.
On the High-Speed Porpoising Instability of a Prismatic Hull
Authors: Payne Peter R.
Published: January 2021

Simple closed-form solutions are obtained for the steady-state and transient forces and moments on a prismatic hull at speeds high enough for hydrostatic forces to be negligible and the chines to be above the undisturbed water surface ("chines dry"). We first show that this solution can be transformed to get the correct results for other hydrodynamic problems, such as the vertical impact of a wedge, a slender foil, or the two-dimensional planing of a flat plate. We then show that the full transient solution is essentially identical with Ribner's [1]2 equations for delta wings, except for terms which depend on the reduction in wetted width with heave. These results are employed to study the stability of such a hull on the assumption that only heave and pitch degrees of freedom are important, following the reasoning of Per̂ing [2]. In contradistinction to all four previous studies [2–5], the effect of skin friction is included and is found to be very powerful. If the center of gravity is above the centroid of the wetted area (which it generally is), then the effect of skin friction is stabilizing.
Base-Vented Hydrofoils of Finite Span Under a Free Surface: An Experimental Investigation
Authors: Verron Jacques , Michel Jean-Marie
Published: January 2021

Experimental results are given concerning the behavior of the flow around three-dimensional base-vented hydrofoils with wetted upper side. The influence of planform is given particular consideration so that the sections of the foils are simple wedges with rounded noses. Results concern cavity configuration, the relation between the air flow rate and cavity pressure, leading-edge cavitation, cavity length, pulsation frequency, and force coefficients.
Added Mass and Damping of Rectangular Bodies Close to the Free Surface
Authors: Newman John Nicholas , Sortland Bjørn , Vinje Tor
Published: January 2021

A submerged two-dimensional rectangle in calm water with infinite depth is studied. The rectangle is oscillating in a heave motion. Negative added mass and sharp peaks in the damping and added-mass coefficients have been found when the submergence is small and the width of the shallow region on top of the rectangle is large. Resonant standing waves will occur in this area. A linear theory is developed to provide a relatively simple explanation of the occurrence of negative added mass for submerged bodies. The vertical hydrodynamic force is associated only with the flow in the shallow region, and the resulting pressure which acts on the top face of the rectangle. The results from this theory are compared with numerical results from the Frank method. The importance of the interaction effect between the top and the bottom of the body, which is neglected in the present theory, is discussed.
Lagrangian Expressions of the Hydrodynamic Forces Acting on a Rigid Body in the Presence of a Free Surface
Authors: Athanassoulis G. A. , Loukakis T. A.
Published: January 2021

The formalism of classical analytical dynamics is used in conjunction with the principle of virtual velocity to derive Lagrangian expressions for the hydrodynamic forces acting on a rigid body moving through an in-viscid and incompressible liquid with a free surface. Simultaneously, a corresponding Lagrangian expression is derived for the hydrodynamic pressure acting on the free surface itself. The expressions for the hydrodynamic forces degenerate to the classical ones if the free surface is not present, and the expression for the pressure is reduced to that obtained by Milder if the rigid boundaries are all kept fixed. The derived Lagrangian expressions for the hydrodynamic reactions are used to obtain a complete set of motion equations for the examined hydromechanical system, and to discuss another Lagrangian approach to the ship-motions problem, presented by Wang.
Dynamics Redesign of Marine Structures
Authors: Hoff Curtis J. , Bernitsas Michael M.
Published: January 2021

The dynamic response of a marine structure depends upon the exciting forces and the modal characteristics of the structure. Excessive vibratory response requires reduction of the exciting loads or redesign of the structure or both. In this paper the general redesign problem is formulated. It applies to large-scale structures and allows for large structural changes. Solution of the redesign problem is achieved through perturbation methods which are an attractive alternative to traditional trial-and-error methods. Perturbation solution methods are based on dynamic equilibrium equations or energy equations or both. A new method based on the energy equations which enforces the mode orthogonality conditions is developed and evaluated against all existing methods. Two test cases, a 191-degree-of-freedom two-dimensional ship model and a 810-degree-of-freedom offshore light tower model are used to compare the methods numerically. It is shown that the method developed in this paper can produce, with a single finite element analysis of the baseline system, a structure which satisfies within acceptable limits all nonconflicting design objectives.
Probabilistic Torsional Vibration Analysis of a Motor Ship Propulsion Shafting System: The Input-Output Problem
Authors: Nikolaidis Efstratios , Perakis Anastassios N. , Parsons Michael G.
Published: January 2021

A probabilistic approach to the torsional vibration analysis of a marine diesel engine propulsion shafting system is developed. The diesel engine and propeller torsional excitation are modeled probabilistically. The statistical properties of the resulting torsional vibratory shear stress in each element of the shafting system are determined by solving the corresponding input-output problem. The shafting system is considered as a multi-input linear system with the propeller and the cylinder torsional excitation as inputs and the torsional vibratory stress as the output. Under the assumption that the nonresonant torsional vibratory stresses are negligible compared with those in resonance, the input-output problem reduces to determining the statistical properties of the output of a multi-input, linear, time-invariant system driven by Gaussian amplitude modulated (AM) processes with equal carrier frequencies. The problem is solved in its general form by deriving an expression relating the double Fourier transform of the output autocorrelation function with the double Fourier transform of the input autocorrelation and cross-correlation functions. The probabilistic approach is applied to calculate the stress statistics in each shafting element of existing low-speed and medium-speed diesel engine propulsion shafting systems.
Transient Motions of Floating Bodies at Zero Forward Speed
Authors: Beck Robert F. , Liapis Stergios
Published: January 2021

Linear, time-domain analysis is used to solve the radiation problem for the forced motion of a floating body at zero forward speed. The velocity potential due to an impulsive velocity (a step change in displacement) is obtained by the solution of a pair of integral equations. The integral equations are solved numerically for bodies of arbitrary shape using discrete segments on the body surface. One of the equations must be solved by time stepping, but the kernel matrix is identical at each step and need only be inverted once. The Fourier transform of the impulse-response function gives the more conventional added-mass and damping in the frequency domain. The results for arbitrary motions may be found as a convolution of the impulse response function and the time derivatives of the motion. Comparisons are shown between the time-domain computations and published results for a sphere in heave, a sphere in sway, and a right circular cylinder in heave. Theoretical predictions and experimental results for the heave motion of a sphere released from an initial displacement are also given. In all cases the comparisons are excellent.
Effective Breadth Problems by an Eigenfunction Approach
Authors: BhaHacharyya Subroto Kumar , Vendhan Chiruvai P.
Published: January 2021

The problem of effective breadth of a stiffened panel with two different edge or support conditions, namely (i) stres -free ed es and (ii) displacement restrained edges, has been solved for the first time, in this paper, by the e.• enfunctoon approach o the end problem of semi-infinite strips. It is shown that these two edge condollens lead to complex eogenvalue problems and thus the plane-stress problem of the plating cannot be solved by the classical methods which have been hitherto successfully used to obtain the estimates of effective breadths for the two other possible mixed edge conditions, namely, (i) vanishing direct stress and tangential displacement and (ii) vanishing normal displacement and shear stress. It is brought out that this end eigenlunetion formulation, using a generalized orthogonality of Papkovich, provides a general analytical framewerk for the stress field problems of stiffened panels in bending. Numerical results are presented for the first problem nly. The two classical problems have been revisited from this viewpoint, and certain well-known effectove breadth results have been rederived and compared. An alternative form of the generalized orthogonality relation, which offers a certain analytical advantage, has been used and the exostence of such a form is proved for all four edge conditions.
An Analytic Approach to Very High Speed Flat Ship Theory
Authors: Cole S. L.
Published: January 2021

This paper defines an asymptotic procedure to generate analytic solutions to the low-aspect-ratio problem of flat ship theory in the limit when the ship is traveling very fast. The leading-order solution terms are worked out, by way of example, for the particular class of hulls with slope fx = -(a + b×) and draft f = -[a(×-y2) + (b/2)(x2-y4)] for y2 ≤ x, 0 ≤ × ≤ 1 with a and b arbitrary constants. A simple expression is worked out in terms of the free constants a and b for the lift and drag and an optimization (over this simple class of hulls) is presented.
Roll of a Ship in Astern Seas—Metacentric Height Spectra
Authors: Dunwoody A. Bruce
Published: January 2021

Unstable roll motions can be a problem in astern seas because of fluctuations in the metacentric height. A formulation for the fluctuations in metacentric height is derived in terms of the distribution of instantaneous wave elevations and wave elevation accelerations along the ship's hull. This formulation is manipulated to derive an equation relating the spectrum of metacentric height fluctuations to the point spectrum of a long-crested, astern sea. Numerical simulations are performed to demonstrate the validity of the method. The singular behavior of the metacentric height spectrum at a frequency of g/4U has implications with respect to the safe operating speeds of a ship in random astern seas.
Modification of Directional Wave Number Spectra by Currents in the Wake of a Surface Ship
Authors: Skop Richard A. , Griffin Owen M. , Leipold Yvan
Published: January 2021

The modification of directional wave number spectra by currents in the wake of a surface ship is examined as a possible cause for the long, narrow region of relatively calm water observed aft of the ship. This region is also seen in radar studies of ship wakes as a suppression of the radar return relative to the radar return from the ambient background. An analysis of the modifications is developed and applied to predicting the radar contrast signature of the wake of a cruiser. The surface wake currents are obtained from computer simulations and model basin tests of a similar vessel. The predictions are compared with quantitative measurements of the radar contrast signature of the cruiser's wake as determined from an L-band synthetic aperture radar. It is found that the wake currents decay much. too rapidly aft of the ship to account for either the magnitude or extent of the measured contrast signature of the calm water region.
Alternative Mathematical Expressions for the Steady Wave Spectrum of a Ship
Authors: Noblesse Francis , Lin Woei-Min , Mellish Robert
Published: January 2021

The study presents a modified mathematical expression for the wave-spectrum function in the Fourier representation of the wave pattern of a ship advancing at constant speed in calm water. This new expression is obtained from the well-known usual expression via several applications of Stokes' theorem resulting in the combining of the integrals along the top waterline and over the hull surface of the ship. The modified expression for the wave-spectrum function is considerably better suited than the usual expression for accurate numerical evaluation because the significant numerical cancellations which occur between the waterline and hull integrals in the usual expression are automatically and exactly accounted for in the modified mathematical expression, as is demonstrated mathematically and confirmed numerically. Whereas the values of both the velocity potential and its gradient at the hull are required in the usual expression for the wave-spectrum function, the new expression only involves the tangential velocity at the hull, not the potential. This new expression thus defines the wave-spectrum function in terms of the speed and the size of the ship, the shape of the mean wetted-hull surface, and the tangential velocity at the mean hull surface. It provides a practical method for coupling a far-field Neumann-Kelvin flow representation with any near-field flow-calculation method, including methods based on the use of Rankine sources or finite differences.
Investigation of the Cone Angle of a Novel Swedged-Stiffened Pressure Hull
Authors: Yuan Kuan-Ya , Liang Cho-Chung , Ma Yung-Chung
Published: January 2021

This paper presents a theoretical analysis of the elastic general instability of two swedged-stiffened cylinders subjected to hydrostatic pressure loading and the effect of varying the angle of the cone section on this general instability pressure. From the standpoint of buckling pressure, available cabin space, and weight reduction, a reasonable cone angle range is proposed.
Modeling of Welding Distortion in Stiffened Rings
Authors: Moshaiov Amiram , Song Haoshi
Published: January 2021

A simple model is developed to describe the deformation of a ring stiffener under welding, with applications to submarine hulls. The model is based on the realization that only a small part of the structure near the welding arc (near field) undergoes high temperature changes, and thus behaves thermo-elastic-plastically, while the rest of the structure (far field) is elastic in nature. The model is used to predict the overall axisymmetric residual shrinkage of different rings and the results are shown to be in excellent agreement with the finite-element method (FEM). This concept of near and far field could also be used to simplify three-dimensional FE models when predicting local, asymmetric welding distortions of various geometry.
Oblique Impact of Two Cylinders in a Uniform Flow
Authors: Guo Zhi , Chwang Allen T.
Published: January 2021

The oblique motion of a circular cylinder through an inviscid and incompressible fluid, conveyed by a uniform flow at infinity, in the vicinity of another cylinder fixed in space is considered. In a relative polar coordinate system moving with the stream, the kinetic energy of the fluid is expressed as a function of six added masses due to motions parallel and perpendicular to the line joining the centers of the cylinder pair. The Lagrange equations of motion are then integrated for the trajectories of the moving cylinder. In order to evaluate the added masses and their derivatives with respect to the separation distance between the cylinders in terms of the hydrodynamic singularities, the method of successive images, initiated by Hicks [1],2 and the Taylor added-mass formula are applied, and analytic solutions in closed form are obtained thereafter. The dynamic behavior of a drifting body in close proximity of a fixed one is investigated by considering the limiting values of the fluid kinetic energy and the interaction forces on each body. The reliability of the numerical approximation of added masses and their derivatives is also discussed in the present study. The integral equations, in terms of surface source distributions and their derivatives on both circles, are carefully modified for obtaining accurate numerical solutions.
Some Numerical Results in 3-D Transient Linear Naval Hydrodynamics
Authors: Pot G. , Jami A.
Published: January 2021

Some numerical results obtained by the code MELINA are given. This code has been designed for the solution of three-dimensional steady and transient flows past a floating or submerged body; the fundamental equations of dynamics are taken into account in the case where the body is freely floating. Only the case of an ocean of infinite depth is addressed here. It is shown that convergence to a steady state is achieved in the case of a periodic forced motion if the history of the motion is correctly taken into account. Also, the case of a freely floating sphere with initial vertical displacement from equilibrium is treated and compared with experiments.
Pontoon Torsional Strength Analysis Related to Ships with Large Deck Openings
Authors: Senjanovic Ivo , Fan Ying
Published: January 2021

The torsional problem of a pontoon, consisting of channel middle part and rectangular tube peaks, isconsidered within the higher-order beam theory. The cross section and the contour compatibility conditions for assembling of the pontoon parts are investigated. The acceptability of the introduced assumptions is checked by three-dimensional finite-element model analysis. Some deficiencies of the classical beam theory regarding the girder stiffness are noticed. The finite-element formulation to be used for the torsional analysis of the ship's hull with large hatch openings is given.
A New Model for Long-Term Stochastic Analysis and Prediction—Part I: Theoretical Background
Authors: Athanassoulis G. A. , Vranas P. B. , Soukissian T. H.
Published: January 2021

A new approach for calculating the long-term statistics of sea waves is proposed. A rational long-term stochastic model is introduced which recognizes that the wave climate at a given site in the ocean consists of a random succession of individual sea states, each sea state possessing its own duration and intensity. This model treats the sea-surface elevation as a random function of a "fast" time variable, and the time history of the spectral characteristics of the successive sea states as a random function of a "slow" time variable. By developing an appropriate conceptual framework, it becomes possible to express various probabilistic characteristics of the sea-surface elevation, which are sensible only in the fast-time scale, in terms of the statistics of sea-states duration and intensity, which is meaningful only in the slow-time scale. As an example, we study the random quantity MU(T) = "number of maxima of the sea-surface elevation lying above the level u and occurring during a long-term time period [0,T]." Exploiting the proposed framework, it is shown that, under certain clearly defined assumptions, Mu(T) can be given the structure of a renewal-reward (cumulative) process, whose interarrival times correspond to the duration of successive sea states. Thus, using renewal theory, the complete characterization of the probability structure of MU(T) is obtained. As a consequence, the long-term probability distribution function of the individual wave height is rigorously defined and calculated. The relation of the present results with corresponding ones previously obtained is thoroughly discussed. The proposed model can be extended twofold: either by replacing some of the simplifying assumptions by more realistic ones, or by extending the model for treating the corresponding problems for ship and structures responses.
Path Control of Surface Ships Using Sliding Modes
Authors: Papoulias Fotis A. , Healey Anthony J.
Published: January 2021

The surface ship path control problem is formulated as a nonlinear state space control problem subject to disturbances, modeling errors, and parameter uncertainty. A "destroyer study" ship using a nonlinear maneuvering model is used as the system model. The system to be controlled is highly nonlinear with parameters that vary with speed and operational conditions. Uncertainty in the force coefficients, as well as in disturbances of the seaway lead to the need for a robust control for navigational accuracy. This paper investigates the use of cross track error and line-of-sight guidance laws with a sliding mode autopilot for path control of surface ships, and presents results based on computer simulations using the model described above. The results illustrate the simplicity and effectiveness of the robust control design for compensating the nonlinearities and disturbance effects with improvements in the navigational accuracy. Comparisons between the two guidance schemes are presented and guidelines are developed with respect to proper guidance selection.
Drag Losses of New Ships Caused by Hull Finish
Authors: Grigson Christopher
Published: January 2021

The performance of finishes representing hull surfaces in trials condition is investigated. The coefficient AC is determined at full scale for many examples. The accuracy of the measurements used to get the actual data on the velocity loss functions Au+ of the surfaces is also investigated. It is sufficient to provide reliable values of AC. The sample of hull finishes is large enough to permit generalization. Provided serious faults of preparation and coating are not permitted, the drag of the finishes is between 2 and 10 percent larger than the perfectly smooth. Thus performance is diverse. The cause is the random topography of low-drag new finishes. The surface features, which are varied, restrict the turbulent fluctuations in the very part of the boundary layer which governs Au+. Variety in surface topography means significant diversity in Au+. Thus, to get AC for trials comparison, the actual loss function of the surface in question must be measured. To get AC for a design at the project stage, the most probable value should be calculated from the data bank of loss functions of new finishes.
Added Masses and Forces on Two Bodies Approaching Central Impact in an Inviscid Fluid
Authors: Landweber L. , Shahshahan A.
Published: January 2021

An integral-equation procedure has been developed to determine interaction forces on two bodies approaching central impact in an inviscid fluid. The accuracy of the results from that procedure is evaluated by applying it to a pair of circles and a pair of spheres for which exact solutions are available. A second purpose was to refine the procedure so that accurate solutions could be obtained at closer distances between the bodies. In the first part of this work, the classical theory is extended by deriving truncation corrections for the infinite series representing the exact solution and asymptotic formulas for computing interaction forces at small gaps. In the second part, two problems were resolved: one on the treatment of the sharp peaks of the integrands when the gap between the bodies was small, the other on reducing the errors in the numerical differentiation required to evaluate the forces. Results for various combinations of circle pairs, for equal spheres, and for an elliptical cylinder approaching a circular one are presented. A new relation between the interaction forces on a wall and on a body moving normal to it is presented.

Addendum published in 1994 Volume 38, Issue 2 (June), pages 172–173, is included.