bluuebunny/crossref_metadata_2025 huggingface dataset:
Dynamics of Coupled Fluid-Structure Multiplate Systems
Authors: Aggarwal K. R. , Sinhasan R. , Grover G. K.
Published: December 2011

A general formulation, for the study of free vibrations and frequency response of a multiplate system fully submerged in fluid contained in an enclosure, has been presented. Although the analytical formulation is suitable for a system consisting of any number of plates submerged in fluid, the present study has been carried out for two-plate systems only. The response of the system is analytically studied when a disturbing force acts on the system through one of the walls of the enclosure in the form of a harmonic wall acceleration. It has been found that the two-plate vibrating system submerged in fluid behaves like a coupled or uncoupled system, depending on the distance between the plates. The fluid coupling effect depends upon the relative positions of plates and walls. It is also observed that the response curves of the two-plate submerged system exhibit the dynamic vibration absorber effect.
2000-hp Motor Support Structure Vibration Sensitivity: Tests, Finite Element Analysis, and Suggested Strategies for Prevention
Authors: Power R. B. , Wood D. E.
Published: December 2011

High vibration was detected during startup of three 2000-hp motors driving critical service compressors. A system natural frequency was close to the running speed. Extensive field tests were conducted; rotor dynamics were studied; and a simple finite element model was made to include the rotor, bearing oil film, motor frame, supporting steel structure, and concrete foundation. Results from the finite element model correlated well with field tests in the areas of natural frequencies, mode shapes, frequency shifts caused by changes in test conditions, transfer functions, and sensitivity to rotor unbalance. Design and procurement strategies to prevent or control future similar problems are proposed.
A Vibration Source in Refrigerant Compressors
Authors: Imaichi K. , Ishii N. , Imasu K. , Muramatsu S. , Fukushima M.
Published: December 2011

During a study of vibrations of a single-cylinder refrigerant compressor of the reciprocating type, which arise after the electric power of the motor is switched off, it was observed that higher frequency damped vibrations arose distinctly in the compressor frame vibrations. This paper shows that the higher frequency damped vibrations observed were caused by torsional and transverse elastic vibrations of the crankshaft which had a rotor of larger mass at one end of the comparatively long and slender shaft. Moreover, it is confirmed that the crankshaft can be one of the major vibration sources which cause higher frequency vibrations of the compressor in constant operation.
Vibrations of Bladed-Disk Assemblies—A Selected Survey (Survey Paper)
Authors: Srinivasan A. V.
Published: December 2011

The progress made in the decade 1973–1983 in the area of vibration of jet engine blades is surveyed. The purpose of the survey is to provide a general review of recent progress and the limited number of references cited can be used to reach the many other important publications in this area. Both structural and aerodynamic aspects of blade vibration are discussed, although the emphasis is on the former. The areas of future analytical and experimental research needed to continue to influence the design of these components are outlined.
A Study of Unsteady Pressures Near the Tip of a Transonic Fan in Unstalled Supersonic Flutter
Authors: Halliwell D. G. , Newton S. G. , Lit K. S.
Published: December 2011

A comparison of experimental and theoretical results is presented for a modern transonic research fan, vibrating in a coupled flutter mode. The measurement of steady and unsteady pressures on the aerofoil surface is described, as also is the derivation of the accompanying blade motion using casing-mounted frequency modulated grids. This complex motion is made use of to calculate unsteady pressures from various unsteady aerodynamic theories. These theoretical models are reviewed in turn and compared against the experimental data at a reference blade section. Considering the complexity of the flow and the inherent simplifying assumptions, the comparisons on both amplitude and phase are generally favorable. The position of the shock in the blade passage is shown to be important. The comparison is extended to unsteady work and again the results are favorable if allowance is made for the differences in blade pressure ratio between the various theories and the experiment.
NASTRAN Forced Vibration Analysis of Rotating Cyclic Structures
Authors: Elchuri V. , Smith G. C. C. , Gallo A. M.
Published: December 2011

Theoretical aspects of a new capability developed and implemented in NASTRAN Level 17.7 to analyze forced vibration of a cyclic structure rotating about its axis of symmetry are presented. Fans, propellers, and bladed shrouded disks of turbomachines are some examples of such structures. The capability includes the effects of Coriolis and centripetal accelerations on the rotating structure which can be loaded with: 1) directly applied loads moving with the structure and 2) inertial loads due to the translational acceleration of the axis of rotation (“base” acceleration). Steady-state sinusoidal or general periodic loads are specified to represent: 1) the physical loads on various segments of the complete structure, or 2) the circumferential harmonic components of the loads in (1). The sinusoidal loads are specified as functions of frequency and the general periodic loads are specified as functions of time. The translational acceleration of the axis of rotation is specified as a function of frequency in an inertial coordinate system. The cyclic symmetry feature of the rotating structure is used in deriving and solving the equations of forced motion. Consequently, only one of the cyclic sectors is modelled and analyzed using finite elements, yielding substantial savings in the analysis cost. Results, however, are obtained for the entire structure. A tuned twelve-bladed disk example is used to demonstrate the various features of the capability.
A Rapid Approach for Calculating the Damped Eigenvalues of a Gas Turbine on a Minicomputer: Theory
Authors: Gunter E. J. , Humphris R. R. , Springer H.
Published: December 2011

The calculation of the damped eigenvalues of a large multistation gas turbine by the complex matrix transfer procedure may encounter numerical difficulties, even on a large computer due to numerical round-off errors. In this paper, a procedure is presented in which the damped eigenvalues may be rapidly and accurately calculated on a minicomputer with accuracy which rivals that of a mainframe computer using the matrix transfer method. The method presented in this paper is based upon the use of constrained normal modes plus the rigid body modes in order to generate the characteristic polynomial of the system. The constrained undamped modes, using the matrix transfer process with scaling, may be very accurately calculated for a multistation turbine on a minicomputer. In this paper, a five station rotor is evaluated to demonstrate the procedure. A method is presented in which the characteristic polynomial may be automatically generated by Leverrier’s algorithm. The characteristic polynomial may be directly solved or the coefficients of the polynomial may be examined by the Routh criteria to determine stability. The method is accurate and easy to implement on a 16 bit minicomputer.
Identification of Vehicle and Collision Impact Parameters From Crash Tests
Authors: Brach R.
Published: December 2011

In the mid 1970s a group of 12 staged and instrumented automobile collisions was conducted for the National Highway Traffic Safety Administration. These were two-vehicle collisions with a variety of initial speeds, vehicle orientations, and vehicle size mixes. Initial speeds were controlled and velocity components including angular velocities at separation were measured. At about the same time, development of the classic theory of impact of rigid bodies to planar vehicle collisions was taking place. Users of classic theory heretofore had neglected the existence of a moment between impacting bodies. Inclusion of a moment and introduction of a moment coefficient of restitution allows the formulation of a planar collision model consisting of six algebraic equations relating the six initial velocity components of the two vehicles to their six final velocity components. The model contains collision geometry, vehicle geometry, vehicle inertial properties, and three coefficients. These coefficients are the classic coefficient of restitution, a friction coefficient, and the newly defined moment coefficient. This paper discusses the application of the theory of least squares to fit the experimentally determined velocity components to the six equations of the vehicle collision model. The usual approach using the theory of least squares is to set to zero the partial derivatives of the sum of squares taken with respect to the unknowns. The original model equations can be added as constraints through the use of Lagrange multipliers. A set of 15 nonlinear algebraic equations results. This approach was tried unsuccessfully. Direct numerical minimization of the sum of squares using gradient projection techniques proved to be far superior. Solutions are obtained for the staged collisions. Results provide insight into velocity changes and their relationships to energy dissipation, the coefficients of restitution and friction and other collision parameters. The capability of calculating velocity changes of colliding vehicles should prove complementary to detailed finite element studies of vehicle crush properties.
The Calculation of the Acoustical Quantities of Railway Wheels
Authors: Irretier H. , Schneider E.
Published: December 2011

The objective of the present investigation is to determine the forced vibrations and acoustical characteristics of a wheel disk with a radially varying thickness from the consideration of axisymmetric and nonaxisymmetric bending vibrations. Using Mindlin’s thick plate theory a finite element approximation to describe the natural vibrations of the disk is applied. The forced response of the wheel is derived as the superposition of the natural modes of vibrations using a modal expansion analysis. With the known vibrating velocity on the surface of the wheel disk the sound pressure and the spatial directivity pattern is determined. The sound power is derived from the numerically integrated acoustical intensity in a surrounding sphere. With the sound power and the space-time mean square velocity, the radiation efficiency of a wheel disk which is harmonically excited at the rim is determined for the whole practical important frequency range.
Recent Modeling of Turbulent Wall Pressure and Fluid Interaction With a Compliant Boundary
Authors: Chase D. M.
Published: December 2011

The relation of wall-pressure amplitude to fluctuating Reynolds-stress source amplitudes in the boundary layer is reviewed for inviscid, slightly compressible flow along a rigid planar boundary. An orthotropic wall-similarity model for source spectra is constructed and applied in this framework to derive a rough model for the wavevector-frequency spectrum of turbulent wall pressure, including radiative wavenumbers. By extension to a compliant boundary, with nonlinear, fluctuating Reynolds stress omitted, an expression is given for fluid-loading impedance and energy exchange in the presence of flow with arbitrary mean velocity profile, in terms of a solution to the homogeneous equation for pressure on a rigid wall. For a compliant boundary driven by fluctuating Reynolds stresses, a formal general relation for wall motion and pressure is derived with a view to the possible effect of nonlinear terms involving wall motion on the amplitude of wall pressure at sub-convective wavenumbers.
An Active Sound Absorber With Porous Plate
Authors: Guicking D. , Lorenz E.
Published: December 2011

An active equivalent of the λ/4 resonance absorber with a porous plate or foil of flow resistance ρc is described. The porous layer is backed by a loudspeaker driven such that zero sound pressure is maintained in the air gap between foil and speaker. The simultaneous control of magnitude and phase has been achieved in analog technique by a combination of open-loop and closed-loop control, utilizing single sideband modulation of the compensation signal with a weak infrasonic auxiliary signal. The on-off ratio of the reflection coefficient reaches −60 dB for sinusoidal sound, and −20 dB for broadband noise.
Static Analysis of Three-Layered Sandwich Cantilever Beams
Authors: Sharma S. R. , Rao D. K.
Published: December 2011

A detailed static deflection and stress analysis of three-layered sandwich cantilever beams, subjected to both uniform as well as concentrated loads, is presented here. Three types of boundary conditions dealing with the mechanism of clamping at one edge and generation of “free” edge condition at the other end are investigated. Various graphs are presented showing the effects of geometric and shear parameters on deflections and stresses. They illustrate how the mechanism of “clamping” at one edge and generation of “free” edge condition can be utilized to increase the stiffness of sandwich beams.
The Effect of Thermoelastic Coupling for Transient Thermal Stresses in a Composite Cylinder
Authors: Takeuti Y. , Furukawa T. , Tanigawa Y.
Published: December 2011

The transient thermal stresses in a composite circular cylinder are examined when the coupling term is taken into account. The solution is valid for the whole time interval without approximation. The numerical results indicate that there is a clear difference between the coupled and uncoupled stress distributions.
Accelerated Cavitation Screening of Organic Coatings Using Acoustic Emission Technique
Authors: Basu S.
Published: December 2011

This paper describes the development of an accelerated cavitation screening method for coatings using the concept of acoustic emission. The analytical models correlating acoustic emission signal properties to measurable cavitation parameters of coatings are described. Some experimental results concerning organic coatings are presented. The analysis of experimental results indicates that the acoustic emission technique is a promising method for the accelerated cavitation screening of coatings. Moreover, the present screening method is an improvement over other existing screening methods in that it has the capability of continuously monitoring cavitation damage. The applicability and limitations of the acoustic emission based screening technique are discussed, and recommendations are made for future research and development work.
Contributions to the Finite Element Solution of the Fan Noise Radiation Problem
Authors: Eversman W. , Parrett A. V. , Preisser J. S. , Silcox R. J.
Published: December 2011

The radiation of fan generated noise to the far field from a nacelle of realistic geometry is investigated using the finite element method. Several innovations have been introduced to minimize the computational requirements and create a highly efficient numerical scheme. The innovations include: (1) formulation of the problem in terms of velocity potential and density in such a way that no inlet mean flow velocity derivatives are required in the field equations, (2) the use of “wave envelope” elements in an outer region permitting a grid much coarser than would be used for conventional finite elements, (3) the use of a mesh which deforms with an increase of forward flight speed so that mesh lines are always lines of constant phase and rays for a point source, permitting the use of wave envelope elements and simple boundary conditions for any case of forward velocity, (4) an efficient scheme for introducing the noise source via modal amplitude coefficients, and (5) the use of a frontal solution technique which for physically realistic problems drastically reduces the active storage requirements. The finite element scheme is outlined, as are the specific details of the innovations. Results are given for cases where comparable experimental data are available.
Energy Propagation Velocity of Elastic Waves in Sandwich Layer
Authors: Ohyoshi T.
Published: December 2011

The explicit characteristic velocities of mechanical energy are obtained in computation for designing structures and acoustical inspections of a sandwich composite plate made of three elastic constituent layers. The dependence of the energy velocity upon the parameters such as ratio of shear velocity, volume fraction, and Poisson’s ratios of constituent layers is discussed in graph form with curves of frequency to energy arrival time. Numerical calculations are carried out up to several higher modes within the range of practical frequencies. The results show that the second mode energy velocity is strongly dependent on the ratio of shear velocity of each constituent layers.
Nominal Stresses in Molded Commutators
Authors: Stokes V. K.
Published: December 2011

Axisymmetric solutions, in which both the radial and hoop stresses undergo a discontinuity, have been used for modeling the nominal stresses in the plastic cores of molded commutators. A model has also been developed for the reduction of nominal stresses by the use of high modulus, high strength, stiffening rings.
The Performance of Jet Noise Suppression Devices for Industrial Applications
Authors: Dahl M. D. , McDaniel O. H.
Published: December 2011

Commercially available jet noise suppression devices were tested to determine their noise reducing characteristics compared to an open pipe. Both exhaust silencers and ejector nozzles were measured for sound power level and mass flow rate. In addition for ejector nozzles, the added noise from a jet impinging on a flat plate was measured. The primary noise generating mechanism for both the open pipe and the silencing devices was due to turbulent mixing, which is dependent upon the velocity. In light of jet noise theory, it will be shown that these devices reduce turbulent noise levels by restricting the flow and creating interactions between small jets. The amount of noise reduction depended upon the design of the silencing device. A large flow reduction was not found to be a necessary criterion for a large noise reduction.
Vibration of a Motor on Viscoelastic Foundation Due to Whirling of the Shaft With Consideration of Electromagnetic Forces
Authors: Nagaya K. , Ikeda S.
Published: December 2011

This paper discusses bending vibration characteristics of a rotating shaft of a motor with consideration of the electromagnetic sucking force which acts on a rotor caused by the narrow electromagnetic field between a stator and the rotor. The dynamic response of the motor under the action of the whirling load of the shaft has been analyzed systematically by considering both the translational and rotary motions of the motor. In the analysis the transfer matrix method is used to obtain the response of the shaft. The equation of longitudinal vibrations of a viscoelastic body is applied to the analysis of the viscoelastic foundation under the assumption of the structural damping. Numerical calculations have been carried out for the natural frequencies, the response of the motor shaft, and the response and the transmissibility of the motor.
The Application of Viscoelastic Passive Damping to Satellite Equipment Support Structures
Authors: Ikegami R. , Johnson D. W. , Walker W. J. , Beck C. J.
Published: December 2011

This paper presents the results of an ongoing study to investigate the use of viscoelastic passive damping technology to decrease the vibroacoustic response of avionics equipment in typical satellite systems. The Inertial Upper Stage, which is subjected to the severe launch vibroacoustic environment of the Space Shuttle and Titan launch vehicles, was selected as the baseline satellite system for this study. The design and analysis of damping treatments were first carried out on a component test structure using finite element analysis and the modal strain energy method. A series of modal survey and acoustic tests on the test structure were performed to validate the analytical procedures and evaluate the effectiveness of the designed damping treatments. The selection and characterization of viscoelastic materials with respect to their performance in space is also discussed.
Automated Analysis of Constrained Systems of Rigid and Flexible Bodies
Authors: Shabana A. A.
Published: December 2011

This paper is concerned with modeling inertia properties of flexible components that undergo large angular rotations. Consistent, lumped and hybrid mass techniques are presented in detail and used to model the inertia properties of flexible bodies. The consistent formulation allows using the finite-element method as well as Rayleigh-Ritz method to describe the deformation of elastic components. Lumped mass techniques allow using shape vectors or experimentally identified data. In the hybrid mass formulation, the flexibility mass matrix is evaluated using a consistent mass formulation, while the inertia coupling between gross rigid body motion and elastic deformation is formulated using a lumped mass technique. Different mass formulations require the evaluation of similar sets of time-invariant matrices that represent the inertia coupling. Consequently, these matrices have to be evaluated only once in advance for the dynamic analysis. A unified mathematical model, and accordingly a unified computer program (DAMS: Dynamic Analysis of Multibody Systems), that deal with different formulations are developed. A comparative study is presented in order to study the effect of the mass formulation on the dynamic response of elastodynamic constrained systems. The validity of the linear theory that neglects the effect of small oscillations on large rigid body motion is also discussed.
Stability of a Rotor Whose Cavity Has an Arbitrary Meridian and Is Partially Filled With Fluid
Authors: Wohlbru¨ck R.
Published: December 2011

The stability of an elastically supported rotor spinning with constant angular velocity is studied. The rotor has a cavity of arbitrary meridian and is partially filled with an ideal fluid. The motions of the system are governed by linearized equilibrium conditions for the rotor and field equations as well as boundary conditions for the fluid. Due to the arbitrary shape of the meridian, it is not possible to solve the boundary value problem in closed form. Therefore a variational expression is developed which satisfies the boundary conditions naturally. The variational problem is solved approximately by the finite element method. The results, incorporated in the equilibrium conditions for the rotor, lead to stability statements. For numerical and experimental investigations, two rotors, one with an elliptical and one with a conical cavity are used. The fill medium is water. There is a close correlation between numerical and experimental results.
Preventive Maintenance for Roller and Journal Bearings of Induction Motor Based on the Diagnostic Signature Analysis
Authors: Koizumi T. , Kiso M. , Taniguchi R.
Published: December 2011

This paper is concerned with the preventive maintenance of roller and journal bearings installed in induction motors. Almost all kinds of failure modes happening on both roller and journal bearings have been reproduced and classified using time and frequency domain data analysis. Diagnostic procedure also has been derived using these analyzed results and statistical method. Finally, an actual diagnostic system for the early stage detection of defected roller bearings has been developed for practical field use.
Determination of Modal Deformations by Means of In Situ Accelerations
Authors: Braun S. , Levran J.
Published: December 2011

Described is a method of extracting modal deflection patterns by means of acceleration measurements only. This enables the testing of systems/machines under normal operating conditions with many potential advantages. A single inertance measurement can be used in conjunction with these results to estimate true modal parameters. The method is demonstrated for a drill under machining conditions. Error associated with the proposed method are discussed, and estimated for the given example.
Reverberation Effects on Directionality and Response of Stationary Monopole and Dipole Sources in a Wind Tunnel
Authors: Baumeister K. J.
Published: December 2011

Analytical solutions for the three-dimensional inhomogeneous wave equation with flow in a hardwall rectangular wind tunnel and in the free field are presented for a stationary monopole noise source. Dipole noise sources are calculated by combining two monopoles 180 deg out of phase. Numerical calculations for the modal content, spectral response and directivity for both monopole and dipole sources are presented. In addition, the effect of tunnel alterations, such as the addition of a mounting plate, on the tunnels reverberant response are considered. In the frequency range of practical importance for the turboprop response, important features of the free field directivity can be approximated in a hardwall wind tunnel with flow if the major lobe of the noise source is not directed upstream. However, for an omnidirectional source, such as a monopole, the hardwall wind tunnel and free field response will not be comparable.
Prediction Method of Gear Noise Considering the Influence of the Tooth Flank Finishing Method
Authors: Masuda Teruo , Abe Toru , Hattori Kanji
Published: December 2011

Simple and accurate prediction methods of gear unit noise have been desired. This paper offers a new prediction equation for spur and helical gears under speed reduction service. A semi-empirical equation was developed by means of the addition of a dynamics term to Kato’s equation which represented the overall noise level by using gear’s specification data. As the proposed method takes into account the gear error characteristics in the vibration analysis of gear pairs, it can calculate the noise levels considering the influence of the tooth flank finishing method. It is shown that the predicted values agree with the measured values in an experiment within a range of approximately 5dB, under almost all the operating conditions and for all test gears having different finishing methods such as hobbing, Niles-type grinding and Maag-type grinding. Moreover, good agreement with data of some actual gear units indicates that the developed method may be used for general application.
The Effect of Limiting Aerodynamic and Structural Coupling in Models of Mistuned Bladed Disk Vibration
Authors: Basu P. , Griffin J. H.
Published: December 2011

A model has been developed for studying the effect of mistuning on bladed disk vibration. Its unique feature is the extent of aerodynamic and structural interaction which it simulates can be readily varied from full coupling of all blades on the disk to coupling of each blade with only its nearest neighbors. Simulations utilizing the resulting algorithm shows that limited coupling models may be used to predict the statistical distribution of blade amplitudes that characterizes the mistuning effect, which in turn determines stage durability. This approach is used to study the effect of changing various system parameters on amplitude scatter. Gas density, the number of blades on the disk, disk stiffness, and the engine order of the excitation are considered. The results are used to draw some conclusions about how to improve laboratory tests and component design.
Application of the Riccati Method to Rotor Dynamic Analysis of Long Shafts on a Flexible Foundation
Authors: Lund J. W. , Wang Z.
Published: December 2011

A method is described for calculating critical speeds, unbalance response and damped natural frequencies of long rotors on a flexible foundation. The shaft and the foundation are calculated separately and coupled at the bearings through impedance matching. Included in the analysis is also a method for representing the shaft response by an expansion in its free-free modes.
Active Vibration Control of a Multimode Rotor-Bearing System Using an Adaptive Algorithm
Authors: Metcalfe A. V. , Burdess J. S.
Published: December 2011

A method for minimizing forced harmonic vibration of a rotor-bearing system by the application of external control forces is presented. The frequency of the vibration is assumed known. In cases of mass unbalance or bend in the shaft this will be shaft rotation frequency and can usually be monitored without difficulty. The control forces could be provided by electromagnetic actuators. The control strategy presented does not require any knowledge of the system parameters and, provided the uncontrolled system is stable, cannot destablize the system. Results from a simulation are shown.
The Effect of Material Heterogeneity and Random Loading on the Mechanics of Fatigue Crack Growth
Authors: Srivatsan T. S. , Sambandham M. , Bharucha-Reid A. T.
Published: December 2011

This paper reviews the experimental work on the influence of variable amplitude or random loads on the mechanics and micromechanisms of fatigue crack growth. Implications are discussed in terms of the crack driving force, local plasticity, crack closure, crack blunting, and microstructure. Due to heterogeneity in the material’s microstructure, the crack growth rate varies with crack tip position. Using the weakest link theory, an expression for crack growth rate is obtained as the expectation of a random variable. This expression is used to predict the crack growth rates for aluminum alloys, a titanium alloy, and a nickel steel in the midrange region. It is observed using the present theory that the crack growth rate obeys the power law for small ΔK and that the power is a function of a material constant.
On Statistical Analysis of Gear Dynamic Loads
Authors: Kumar A. S. , Osman M. O. M. , Sankar T. S.
Published: December 2011

Statistical analysis of the gear dynamic load is carried out using piecewise constant mesh stiffness approximation. The dynamics of the spur gear system is modeled as a nonlinear, nonstationary process, and the gear transmission error which acts as a random input to the gear system is generated by passing a Gaussian white noise process through a time invariant shaping filter. The equivalent discrete time state equation and the mean and covariance propagation equations are then written for the augmented system. Then starting from known initial conditions these propagation equations are used to compute the statistics of the steady state response and hence those of the dynamic load. A procedure is presented for the selection of proper initial conditions so as to reach the steady state condition faster, thereby reducing the computational time required. The variations in the statistics of the dynamic load with respect to changes in contact position, random error magnitude, and operating speed are also investigated with the help of a numerical example. The results show that the approach presented in this study provides truer results than the statistical linearization approach used by Tobe et al. [13]. Moreover, the proposed procedure has the advantage that it can be applied to higher-order systems with complex mesh stiffness and torque fluctuations and to systems with symmetrical or nonsymmetrical nonlinearities.
Analysis of a Bolted Flange With Eccentric Loading
Authors: Riemer M. , Taschner R. , Pavelic V.
Published: December 2011

A new method is presented for the analysis of a bolted flange subjected to bending moments. Bolt axial cyclic loads are calculated using the force ratio method. Bolt bending moments are found with the new analysis scheme presented. A key factor in the analysis is the area in compression of the flange. Experimental results are used to substantiate the theoretical methods. A finite element analysis was also conducted to support the theory.
Rapid Measurement of Modal Properties Using FFT Analyzers With Random Excitation
Authors: Cawley P. , Rigner L. G.
Published: December 2011

The use of a Nyquist plot of the H2 (Syy/Sxy*) frequency response function estimates produced by an FFT based spectrum analyzer with random excitation to obtain modal amplitudes and hence modal constants has been investigated. It has been proved that, irrespective of the frequency resolution used, the H2 estimates always lie on the true modal circle so even at coarse frequency resolution, a circle fitted to these points gives accurate values of modal amplitude. The conventional H1 (Sxy/Sxx) estimates lie inside the true modal circle. Use of the H2 technique results in major savings in the testing time required for a modal survey, particularly when measurements are to be taken at many points on the test structure.
Autoparametric Vibration of Coupled Beams Under Random Support Motion
Authors: Ibrahim R. A. , Heo H.
Published: December 2011

The dynamic response of a two degree-of-freedom system with autoparametric coupling to a wide band random excitation is investigated. The analytical modeling includes quadratic nonlinearity, and a general first-order differential equation of the moments of any order is derived. It is found that the moment equations form an infinite hierarchy set which is closed via two different closure methods. These are the Gaussian closure and the non-Gaussian closure schemes. The Gaussian closure solution shows that the system does not reach a stationary response while the non-Gaussian closure solution gives a complete stationary steady-state response. In both cases, the response is obtained in the neighborhood of the autoparametric internal resonance condition for various system parameters.
On the Applications of the Boundary-Element Method to Acoustical Field Studies of Vibrating Structures
Authors: Jiang J. K. , Prasad M. G.
Published: December 2011

This paper describes the applications of the Boundary-Element Method (BEM) for studies on acoustical field of various vibrating structures. The studies emphasize the numerical aspects of the BEM. Both acoustical near and far fields of the vibrating structures are investigated in this work. The vibrating structures considered in this application studies are a circular piston in an infinite, rigid baffle and cantilever-type beams. In the case of piston in an infinite baffle, instead of using the method of images, the free-space Green’s function is used to evaluate boundary integral equation by including both piston and baffle surfaces. The influence of the stationary baffle in the case of piston is further investigated. The beams considered are of both rectangular and circular cross sections. The results obtained by BEM have compared well with the available results from classical methods. The studies indicate that in the application of BEM in such problems both the element size and the number of elements including stationary surface have significant effect on the results obtained. The studies have yielded that very good results are obtained when the largest dimension of an element is equal to 0.2 times the acoustic wavelength (in air) of the frequency of acoustic radiation.
A New Approach for the Identification of a Regression Locus for Estimating CDF-Failure Equations on Rectified Plots
Authors: Mischke C. R.
Published: December 2011

In estimating the cumulative density function of data, investigators selectively transform the data and their order statistics in order to achieve rectification of the data string. Ordinary least-squares regression procedures no longer apply because of the transformations. Investigators are often seeking a fifty-percent (median) locus, which least-squares methods do not ordinarily discover. A weighted least-squares regression procedure is presented that will establish an estimate of the mean CDF line and through appropriate rotation, provide an estimate of the median CDF line. Examples from common distributions follow a general development.
Design with Nonhomogeneous Materials—Part II: Torsion of Thin-Walled Prismatic Bars
Authors: Stokes V. K.
Published: December 2011

Theories have been developed for the torsion of nonhomogeneous thin-walled prismatic bars of open section and thin-walled tubes. The mechanical response of these members has been shown to be equivalent to the corresponding homogeneous case with the modulus of rigidity replaced by a suitable average of the variable rigidity modulus of the material. These average moduli, which are different for each geometry, are shown to be moments of the variable modulus of the nonhomogeneous material. Interpretations for the average moduli, which would be determined by torsion tests on nonhomogeneous materials, have been considered.
Application of Transfer Matrix Method to Analysis of Transient Response of Beam
Authors: Goya Moriaki , Hayashi Takuo , Ito Koichi , Ohki Hiroshi
Published: December 2011

The transient responses of an elastic beam to large dynamic deformations were analyzed numerically, using the transfer matrix method. Geometrically nonlinear differential equations were linearized by introducing increments of unknown functions, and the resulting linear equations were approximated by finite difference equations. A field transfer matrix was introduced for the analyses of large deformations; this determined the relationship between the incremental state vectors at both ends of the elastic segments. The Newmark β formulation was chosen to approximate the equation of motion for concentrated masses. A concentrated mass point transfer matrix and an inhomogeneous vector were introduced for analyses of the transient responses of the beams. A superposition scheme for the transfer matrix method was proposed as an effective means of obtaining a solution satisfying the boundary conditions at both ends of the beam.
Vibrational Energy Transmission and Mode Conversion at a Corner-Junction of Square Section Rods
Authors: Gibbs B. M. , Tattersall J. D.
Published: December 2011

The low frequency reflection and transmission of vibrational energy at an L-junction of square section rods is investigated theoretically and experimentally. The theoretical description, in which thin rod theory is employed, is complete in that all modes of vibration are considered including compression, torsion, and bending both for the incident and generated waves. It is seen that bending vibration in the plane of the system is coupled to compressional waves and bending vibration normal to the plane of the system is coupled to torsional waves. The theory applies to junctions of semi-infinite rods and this condition was simulated experimentally by means of impulse response techniques in which the reflected waves were removed by truncating the time histories prior to frequency analysis. A novel combination of phase separation, time of flight methods, and filtering has allowed the various modes of vibration to be separated and the agreement between predicted and measured reflection and transmission loss, both for same mode and dissimilar mode coupling, is promising.
Load Distribution of Parallel Springs With Random Length and Stiffness
Authors: Gerbert Go¨ran , de Mare´ Jacques
Published: December 2011

There are many applications in mechanical design where load distribution is modelled with parallel springs. Here random variation in spring length and spring stiffness is considered. Length variation is assumed to be the major influence and the case with uniform distribution is analyzed in detail. Small variations in spring stiffness are included. Numerical results are given. A simple formula is presented which gives the maximal length deviation as a function of the number of springs. The formula is based on a 10 percent failure risk which is a common number in practical mechanical design.
Response Bounds for Damped Linear Mechanical Systems Under Prescribed Motion
Authors: Nicholson David W.
Published: December 2011

In earlier investigations, the author used extensions of two theorems of G. Strang to derive bounds on the displacements of a symmetric damped linear mechanical system subject to prescribed periodic forces. This work is extended in the current investigation to obtain bounds under prescribed periodic motions. For prescribed periodic forces, the bounds were expressed in terms of the extreme eigenvalues of several symmetric, positive definite matrices. In contrast, in the current case the bounds also depend on several nonsymmetric matrices. The bounds under prescribed motion are evaluated in an example and comparison is made with an exact result. The results reported here are new.
An Eigensystem Realization Algorithm in Frequency Domain for Modal Parameter Identification
Authors: Juang J.-N. , Suzuki H.
Published: December 2011

This paper demonstrates the close conceptual relationships between time domain and frequency domain approaches to identification of modal parameters for linear systems. A frequency domain eigensystem realization algorithm, via transfer functions, is developed using a known procedure formulated for a time domain eigensystem realization algorithm, via free decay measurement data. An important feature is the capability of windowing to concentrate analysis on the frequency range of interest. The procedure of overlap averaging is used to produce smoother spectra to reduce the effect of noise on identified modal parameters. Examples from simulation and experiments are given to illustrate the validity of formulations derived in the paper.
The Effects of Elastic Deformation on Seal Dynamics
Authors: Iwatsubo T. , Yang B. S.
Published: December 2011

The dynamic characteristics and stability of the annular pressure seal employed in pumps have been theoretically deduced with consideration of the effects of elastic deformation due to the high pressure difference. Turbulent flow is assumed in both circumferential and axial direction, and the deformation of the seal and the shaft is governed by the linear theory of elasticity. The results derived herein considering the elastic deformation are compared with the previously published author’s results [3] in the stiffness, damping, and add mass coefficients.
Aperture Effects in Planar Nearfield Acoustical Imaging
Authors: Hayek S. I. , Luce T. W.
Published: December 2011

The influence of the size of the measurement aperture on the accuracy of reconstruction of the pressure and vector velocity fields using underwater nearfield acoustical holography technique is examined. In this measurement technique, the amplitude and phase of the pressure in the nearfield of a planar structure submerged in water is measured at a set of points on a planar surface which constitute the measurement aperture. The reconstruction of the pressure and velocity vector fields on the surface of a vibrating submerged steel plate was found to be insensitive to the aperture size down to the size of the structure. Examples of aperture sizes ranging from six (6) times down to 1/2 of the size vibrating steel plate are shown. Thus, the total length of time spent on measurements underwater can be drastically reduced.
Aerodynamic Indicial Response and Stability Derivatives of a Rotor Annulus
Authors: Mengle V. G.
Published: December 2011

The key to finding the aerodynamic forces acting on a rotor in arbitrary rigid-body motion is its response to indicial input of its individual degrees of freedom. A theory is developed to find such indicial responses for an unloaded rotor annulus moving in its own plane. New rational approximations in the complex-frequency domain are used to find the corresponding transient cascade forces for incompressible flow. The indicial response consists of an initial impulse and an oscillatory decaying part for force components parallel and perpendicular to the applied motion. The harmonic response is also found and is expressed in terms of complex “rotor-stability-derivatives,” which are essentially the direct-and cross-coupled frequency dependent damping or stiffness force coefficients. Both responses are obtained explicitly in terms of the unsteady cascade characteristics and reduced frequency or time. Parametric studies indicate lowered damping, aerodynamic spring-softening and cross-stiffness whirling forces dependent on the upstream dynamic pressure for perturbation frequencies near the rotor speed.
The Dynamics of an Impact Print Hammer
Authors: Tung P. C. , Shaw S. W.
Published: December 2011

A mathematical model is developed to describe the characteristic behavior of an impact print hammer of the stored energy type. The armature of the impact print hammer is represented by a rigid mass held against a backstop by a preloaded linear spring with negative stiffness which characterizes the net effect of a permanent magnet and a prestressed flexible beam acting on the armature. Periodic sine pulses are adopted to represent currents which release the armature to strike the ribbon and paper which is represented by a linear spring and a linear viscous dashpot. A coefficient of restitution is employed to characterize the instantaneous behavior of impact and rebound at the backstop. In this paper, periodic motions with n impacts against the backstop per forcing cycle, period doubling bifurcations, and chaotic motions are found. The stability of the periodic motions is investigated as is the influence of various parameters on the performance of the impact print hammer. With this simple model we can predict much of the qualitative behavior of the actual physical system.
Electromagnetic Control of Oil-Film Supported Rotors Using Sparse Measurements
Authors: Burrows C. R. , Sahinkaya M. N. , Clements S.
Published: December 2011

An electromagnetic controller is applied to a flexible rotor supported by two oil-film bearings. The synchronous vibration is controlled by using a combined estimation and optimization algorithm. This requires no a priori knowledge of the system model. The effect of using a limited number of measurement sites on the controller performance is assessed. Optimum measurement sites are defined. The results of both computer simulations and experimental studies are presented. It is shown that the strategy developed by the authors can reduce the synchronous vibration to less than 10 percent of the uncontrolled response. The open-loop adaptive strategy can be applied to reduce the time required for in-situ tuning of magnetic controllers.
Excitation Force Identification of Rotating Machines Using Operational Rotor/Stator Amplitude Data and Analytical Synthesized Transfer Functions
Authors: Verhoeven J.
Published: December 2011

Hydraulic excitation forces of rotating machinery are normally determined by direct measurement techniques like strain gages, load cells, etc. This paper presents an indirect method, in which frequency response transfer functions are analytically generated, using linear rotor/stator models. Inverse transfer function matrices are multiplied with operational vibration data to yield fourier transformed operational excitation forces. Analytical excitation techniques and numerical inversion methods of the system transfer function matrix are evaluated. External error sources and guidelines for an error sensitivity analysis of the predicted forces are described. Experimental verification is presented on a large horizontal centrifugal pump, with reasonable results. Typical application is shown on multistage hydro carbon and boilerfeed pumps.