bluuebunny/crossref_metadata_2025 huggingface dataset:
Precession of Vibrational Modes of a Rotating Hemispherical Shell
Authors: Hwang J. J. , Chou C. S. , Chang C. O.
Published: February 2008

The precession of flexural vibrational modes of a rotating hemispherical thin shell is investigated. Niordson’s thin shell theory, which allows the stretch of the middle surface, is employed to derive the equations of bending vibration of a rotating shell. The shell is assumed to rotate at a low constant speed, so the centrifugal force is neglected and only the Coriolis inertial force is included in the equations of motion. The ratio of the rotating speed of the shell to the natural frequency of the first flexural mode, which is denoted by ε, is assumed small. The solutions of displacements are expanded in the power series of ε. The unperturbed (zero-order) equations, which represent the free vibration of the nonrotating shell, are proved to be self-adjoint. The perturbed frequency can be extracted from the equation of solvability condition directly without solving the perturbed system. The precession rate of the vibrational modes obtained theoretically in an analytical expression is verified by experiment. These results are helpful for the design of hemispherical resonant gyroscope.
On an Innovative Method of Modeling General Nonlinear Mechanical Systems, Part 2: Experiments
Authors: Xu K. Q. , Rice H. J.
Published: February 2008

In this the second part, the attention will he focused on the practical implementation of the techniques proposed in Part 1. Firstly, the problem of generating a periodic excitation signal with a specific spectrum in the experimental conditions will be solved by the use of a programmable signal analyzer. Secondly, using this spectral control technique and applying the generalized linear path identification method proposed in Part 1, two simple nonlinear structures are tested and analysed. Finally, the application of this new package of nonlinear system identification techniques is experimentally demonstrated on a multiple DOF structure. It includes the practical implementation of the spectral controller, the generalized linear path identification method, the practical location scheme of nonlinear elements and the in-situ nonlinear force state mapping technique.
Sensitivity of a Mobile Manipulator Response to System Parameters
Authors: Akpan U. O. , Kujath M. R.
Published: February 2008

The reported study investigates the stochastic dynamics of a mobile manipulator. The manipulator is mounted atop a vehicle supported on multiple wheels. Stochastic excitations and deterministic excitation of the manipulator are induced by the acceleration of the vehicle on a traction surface. The stochastic excitations are related by time delays due to the longitudinal alignment of the vehicle wheels. Expressions for the deterministic and covariance matrices of the manipulator stochastic motions are developed. Sensitivity of the system responses to the surface roughness, the dynamics and the kinematics parameters of the manipulator is investigated. Suggestions for mobile manipulator design to minimize the influence of the stochastic base excitations are presented.
Damping of Flexural Waves With Imbedded Viscoelastic Materials
Authors: Marsh E. R. , Hale L. C.
Published: February 2008

This paper considers a passive damping method that can be applied to beam-like structures such as machine tool bases and columns. The method uses viscoelastic materials to dissipate energy in the manner of classic constrained-layer damping; however, the layers are embedded within the structure as opposed to being applied externally. This provides a robust means of incorporating damping without encountering several of the common disadvantages associated with external damping treatments. An analytical solution to the amount of damping that can be achieved using embedded layers is available, but is known to be inaccurate when the viscoelastic stiffness approaches that of the structural components. Therefore, a new prediction of the maximum damping level that can be expected in a structure is developed and presented here. This prediction gives good results in a wide variety of applications, and offers insight into the relationship between key design parameters. Finite element and experimental verification of the maximum damping predictor are also presented.
Planar Motion of a Flexible Beam With a Tip Mass Driven by Two Kinematic Rotational Degrees of Freedom
Authors: Winfield D. C. , Soriano B. C.
Published: February 2008

The objective was to model planar motion of a flexible beam with a tip mass that is driven by two kinematic rotational degrees of freedom which are (1) at the center of the hub and (2) at the point the beam is attached to the hub. The equations of motion were derived using Lagrange’s equations and were solved using the finite element method. The results for the natural frequencies of the beam especially at high tip masses and high rotational velocities of the hub were calculated and compared to results obtained using the Raleigh-Ritz method. The dynamic response of the beam due to a specified hub rotation was calculated for two cases.
A Theoretical Model to Predict Vibration Response of Rolling Bearings to Distributed Defects Under Radial Load
Authors: Choudhury A. , Tandon N.
Published: February 2008

An analytical model has been presented to predict the vibration response of rolling bearings due to distributed defects under radial load. For bearings without defect and with race defect, the model predicts a discrete spectrum with components at outer and inner race characteristic defect frequencies for the response of the respective races. The amplitude level for race defect significantly increases at the respective frequencies in comparison to the response of a bearing without defect. For a bearing with off-size rolling element, the response is at the relative frequency of cage with respect to the frequency of motion of the corresponding race.
Modeling and Control of an Electrorheological Sandwich Beam
Authors: Rahn C. D. , Joshi S.
Published: February 2008

This paper introduces models for electrorheological (ER) structures based on visco-elasticity and sandwich beam theory. The partial differential equations describing the dynamics of an ER sandwich beam are derived and a modal analysis is performed. Feedback controllers, derived using Lyapunov theory, ensure stability of all modes of the beam. Feedback from an axial velocity sensor to the applied ER beam voltage provides an implementable approximation to the control law. Simulations of a cantilevered ER beam show the stable response and improved transient decay provided by the control system.
Split Vibration Modes in Acoustically-Coupled Disk Stacks
Authors: Tseng J.-G. , Wickert J. A.
Published: February 2008

Vibration of an array of stacked annular plates, in which adjacent plates couple weakly through an acoustic layer, is investigated through experimental and theoretical methods. Such acoustic coupling manifests itself through split natural frequencies, beating in the time responses of adjacent or separated plates, and system-level modes in which plates in the array vibrate in- or out-of-phase at closely-spaced frequencies. Laboratory measurements, including a technique in which the frequency response function of all in-phase modes but no out-of-phase modes, or visa versa, is measured, demonstrate the contribution of coupling to the natural frequency spectrum, and identify the combinations of design parameters for which it is important. For the lower modes of primary interest here, the natural frequencies of the out-of-phase system modes decrease as the air layer becomes thinner, while those of the in-phase mode remain sensibly constant at the in vacuo values. A vibration model comprising N classical thin plates that couple through the three-dimensional acoustic fields established in the annular cavities between plates is developed, and its results are compared with measurements of the natural frequencies and mode shapes.
Galloping Limit Cycle Amplitude and Frequency Estimation
Authors: White W. N. , Lynch P. M. , Venkatasubramanian S. H.
Published: February 2008

The amplitude, frequency, and mode shape of a single galloping conductor are estimated. A finite element model of the line and supports based upon the weighted residual method is presented. The results produced by the analysis show good agreement with results obtained elsewhere. It is demonstrated that the fundamental galloping frequency can be aerodynamically dependent. Also included in the model are compliant line supports to represent the towers.
On Free Vibrations of Fiber Reinforced Doubly Curved Panels, Part 1: Formulation/Convergence Study
Authors: Singh A. V. , Kumar V.
Published: February 2008

This paper presents a Ritz-type numerical scheme for the analysis of doubly curved laminated open panels. The fundamental strain-displacement relations and energy expressions are developed in orthogonal curvilinear coordinates. Higher-order shear deformation theory and the effects of rotary inertia are included in the formulation. The displacement fields are prescribed by Bezier surface patches and the procedure to implement the boundary conditions in this context is also described. The numerical method is developed such that any arbitrary open panel bounded by four curved edges can be analyzed. Two examples namely: cantilevered cross-ply cylindrical and spherical panels are used to demonstrate the convergence of the solution procedure. Bezier surface patches formed by the eighth order polynomials yield good values of the natural frequencies.
Application of Multiple Scale Analysis on the Parametric Resonance of Continuous Gyroscopic Systems
Authors: Chen Jen-San , Lin Yu-Ran
Published: February 2008

Nayfeh and Mook (1977) presented a multiple scale analysis on the parametric resonance of a non-gyroscopic system with multiple degrees of freedom. This Note extends their method to the case of continuous gyroscopic systems Orthogonality properties among the eigenfunctions of the unloaded system in the complex state space are used to discretize the equation of motion into a set of first order differential equations. Multiple scale method is then employed to study the parametric resonance of the loaded system up to the second order perturbation. A spinning Rayleigh beam under pulsating axial load is studied as an example.
Dynamic Response and Stability of Pressurized Gas Squeeze-Film Dampers
Authors: Arakere N. K. , Ravichandar B. C.
Published: February 2008

Compressible squeeze films, an important and interesting area in gas lubrication, have been relatively neglected in recent times. Aircraft engines are being designed with light weight flexible rotors operating at high speeds and temperatures that may eventually eliminate the use of oil lubrication. A gas or air SFD might be a viable alternative to a conventional oil damper, in high temperature applications that preclude the use of oil lubrication. Oil squeeze-film dampers currently being used for rotordynamic control will not be viable at temperatures above 350°F, due to limitations on lubricant oil temperature. A good example of gas SFD application is in conjunction with high temperature gas lubricated foil bearings, which inherently have low damping. This paper presents an analysis of pressurized air dampers, similar to a hydrostatic gas bearing. Pressurized air is supplied through a series of orifices in the bearing midplane. Airflows through the orifices and the resulting pressure forces are calculated using a simple gas-flow model, as in orifice compensated hydrostatic bearings. A small perturbation analysis of the shaft center yields the stiffness and damping coefficients, for centered circular orbits. Damping characteristics are studied for a range of parameters such as supply pressure, orifice diameter, pocket volume, orbit size, number of orifices and shaft speed. Results show that maximum damping forces are generated for near choking flow conditions. The damping coefficient becomes negligible at frequencies above 350 Hz. For damping force to be present, the gas pressurization has to exert a force on the rotor opposing the instantaneous velocity, or, 90 degrees out of phase with displacement. Linear stability of unbalanced dampers undergoing centered circular orbits, is also investigated, in view of their relevance to rotordynamics. Damper design curves are presented for various parameters.
Unbalance Response of a Flexible Rotor Supported by a Squeeze Film Damper
Authors: Zhao J. Y. , Linnett I. W. , McLean L. J.
Published: February 2008

This paper investigates the unbalance response of a squeeze film damper-mounted flexible rotor, Both concentric and eccentric damper operations are examined. Comparison between predicted and experimental results shows that the ’0’ film model is preferred to the π film model. Near the first pin-pin critical speed the ’0’ film model underestimates the damping effect and overestimates the centralizing force of the damper. By choosing a lower film rupture pressure in the theoretical model, better matches to the experimental results are obtained. The effects of air entrainment are shown to produce unsteady responses and jump phenomena of softening spring type. It is concluded that damper models having constant film rupture pressures do not truly represent the cavitation problem in squeeze film dampers.
Dynamics of a Flexible Beam With Active Nonlinear Magnetic Force
Authors: Tseng Chyuan-Yow , Tung Pi-Cheng
Published: February 2008

A simply supported beam is controlled in a contactless manner by the attractive force of magnetic actuators that are controlled by feedback signals from displacement and velocity sensors to stabilize the levitation. The equations of motion for the single mode of a beam’s model are used to show that due to the realistic nonlinear terms existing in the magnetic force, the resulting third-order system exhibits codimension-two bifurcations in which a limit cycle and a heteroclinic orbit are created. Using the bifurcation analysis, it was determined how feedback gains influenced the behavior of transverse vibrations of the beam and the feedback gains producing stability were found. The largest region of attraction of those stable regions is showed to exist at certain feedback gain combination. The analytical approach based on the single mode simplification system was proven to be feasible via the numerical simulation of the governing nonlinear PDE. According to the results of the analysis, due to the nonlinear magnetic force, feedback gains for the system must be selected carefully.
The Efficacy of the Momentum Balance Method in Transverse Impact Problems
Authors: Yigit A. S. , Christoforou A. P.
Published: February 2008

An elastic-plastic contact law that incorporates local permanent deformation in the contact zone has been used to investigate the efficacy of the momentum balance method in transverse impact problems. The momentum balance solution is compared to the numerical solution of the same equations using the contact law. It is shown that the momentum balance method gives very good results for the post impact behavior of both the impacter and the beam. In certain cases, it is also shown to yield satisfactory results for the dynamic behavior during contact. It is demonstrated that the momentum balance method with an appropriate coefficient of restitution obtained from the contact law, is physically the same as using the contact law itself, with the difference that the local deformation is neglected.
Monitoring Torsional Vibrations of Electro-mechanical Systems Using Stator Currents
Authors: Yacamini R. , Smith K. S. , Ran L.
Published: February 2008

A method is proposed to detect shaft torsional vibrations in AC motors and generators from their stator currents. This is achieved by extracting current components at specific frequencies which are the modulation products of the power system frequency and the vibrating frequency. A general closed form proof of this principle is given for both induction and synchronous machines, and the principle is verified quantitatively by digital simulation and experimental results. The effect of the machine operating point is also investigated. The method is applicable to torsional vibrations induced by different causes. When the oscillating torque is developing and the measured stator current is nonstationary, the Wavelet Transform can be used to extend the application of the proposed method to transient conditions.
A New Rectangular Plate Element for Vibration Analysis of Laminated Composites
Authors: Qian Guan-Liang , Hoa Suong V. , Xiao Xinran
Published: February 2008

In this paper, a higher order rectangular plate bending element based on a Higher Order Shear Deformation Theory (HSDT) is developed. The element has 4 nodes and 20 degrees of freedom. The transverse displacement is interpolated by using an optimized interpolation function while the additional rotation degrees of freedom are approximated by linear Lagrange interpolation. The consistent element mass matrix is used. A damped element is introduced to the finite element model. The proposed FEM is used to calculate eigenfrequencies and modal damping of composite plates with various boundary conditions and different thicknesses. The results show that the present FEM gives excellent results when compared to other methods and experiment results, and is efficient and reliable for both thick and thin plates. The proposed finite element model does not lock in the thin plate situation and does not contain any spurious vibration mode, and converges rapidly. It will provide a good basis for the inverse analysis of vibration of a structure.
Nonaxisymmetric Acoustic Radiation and Scattering From Rigid Bodies of Revolution Using the Surface Variational Principle
Authors: Ginsberg J. H. , Wu Kuangcheng
Published: February 2008

The surface variational principle (SVP), which represents the surface response as a series of basis functions spanning the entire surface, provides a global description of acoustic fluid-structure interaction that has many of the benefits associated with analytical methods. This paper describes the extension of SVP to model the interaction between the velocity and pressure on the surface of an axisymmetric body subjected to nonaxisymmetric excitation. Problems addressed are radiation due to arbitrary rigid body motion, and scattering associated with arbitrary incidence of a plane wave on a stationary rigid body. Numerical results are presented for flat-ended and hemi-capped cylinders. These results are compared to those obtained from the CHIEF-88 and SHIP-92 computer codes. The convergence properties of SVP are examined in detail, particularly for its requirements when ka is in the upper part of the mid-frequency range.
Identification of Properties of Nonlinear Joints Using Dynamic Test Data
Authors: Ren Y. , Lim T. M. , Lim M. K.
Published: February 2008

This paper presents a general purpose technique for identifying (extracting) the dynamic properties of nonlinear joints using dynamic test data. No theoretical model is required, only experimental data are needed for the identification. Because no assumption on the properties of the nonlinear joints is made, the method is applicable for identifying almost any type of nonlinear joints. In the identification method, the nonlinear force at a joint is treated as an external force and the principle of multi-harmonic balance is employed. The force-response relationship of a nonlinear joint is then obtained. Various measurement errors in experimental data can affect the accuracy of identification. In this paper, efforts are also devoted to understanding how the accuracy of identification is affected by measurement errors. Techniques for improving the accuracy of identification are also discussed. The method is verified by experimental studies. The nonlinear properties of an impact joint and a friction joint have been successfully identified.
Fatigue Life Prediction of Nonlinear Plates Under Random Excitations
Authors: Sun J. Q. , Bao W. , Miles R. N.
Published: February 2008

An efficient method is presented for estimating the high cycle fatigue life of nonlinear structures under random excitations. The procedure is based on an application of the method of equivalent linearization for constructing the response of the stress of the structure in time domain. Fatigue estimates are obtained by processing the time domain signal using the Rain-Flow cycle counting scheme in conjunction with the linear accumulative damage theory. The estimated average fatigue life of a nonlinear plate under random excitations by the present method is compared with the result obtained by direct Monte Carlo simulations of the original nonlinear modal equations. The agreement is excellent for a wide range of levels of nonlinearity. The present method has the advantage of being much more computationally efficient than direct numerical simulations of nonlinear systems. The computational effort required of the present method for a nonlinear system is nearly the same as that for a linear system and is not affected much by the type and level of nonlinearity in the structure. The present method offers a practical means for predicting high cycle fatigue lives of complex nonlinear structures.
A Detailed Mechanical Model of a Double Pumper Fluid Mount
Authors: Vahdati N.
Published: February 2008

Conventional passive elastomenc mounts have been used as noise and vibration isolators in the automotive and aircraft industries for many years. For even better noise and vibration isolation, passive fluid mounts have been replacing elastomeric mounts in both the automotive and aerospace industries during the past few years. With more increase in the popularity of fluid mounts, it is important to characterize the dynamics of the fluid mounts more accurately. Many papers have been published on the modeling of these devices, but mostly on single pumper fluid mounts. In this paper, we focus on double pumper fluid mounts. The intent of this paper is to develop a very detailed model of a double pumper fluid mount including all dampings.
A Vibrational Mode Analysis of Free Finite-Length Thick Cylinders Using the Finite Element Method
Authors: Wang Huan , Williams Keith , Guan Wei
Published: February 2008

Based on their three-dimensional mode shapes, the vibrational modes of free finite length thick cylinders can be classified into 6 categories, consisting of pure radial, radial motion with radial shearing, extensional, circumferential, axial bending, and global modes. This classification, together with the numbers of both the circumferential and the longitudinal nodes, is sufficient to identify each mode of a finite length thick cylinder. The mode classification was verified experimentally by measurements on a thick cylinder. According to the displacement distribution ratio in the radial, tangential and longitudinal directions, the effect of varying cylinder length on the vibrational modes is such that all the modes can be broadly categorized as either pure radial modes, or non pure radial modes. The natural frequencies and mode shapes of the former are dependent upon only the radial dimensions of the models, while the natural frequencies and mode shapes of the latter are dependent upon both the axial length and radial thickness.
Mid-Frequency Range Acoustic Radiation From Slender Elastic Bodies Using the Surface Variational Principle
Authors: Wu K. , Ginsberg J. H.
Published: February 2008

The surface variational principle (SVP) yields analytical-type results for radiation and scattering from submerged bodies whose shape does not suit classical techniques for analyzing the Helmholtz equation. The approach employs Ritz series expansions for surface pressure and velocity in the frequency domain. The relation between the series coefficients is obtained by extremizing the SVP functional. The present work extends the earlier developments to the case of an axisymmetric elastic shell that is subjected to an arbitrary excitation. The surface pressure and normal velocity are represented as a sequence of surface waves that are the trace of the waves in the surrounding fluid medium. SVP is used to determine the wavenumber spectrum of pressure amplitudes generated by a specific wave having unit velocity amplitude. The structural displacement field is also represented by Ritz expansions, and equations governing the generalized coordinates associated with these series are obtained by invoking Hamilton’s principle. Difficulties in satisfying the continuity conditions at the apexes are circumvented by selecting basis functions that map spherical shell eigenmodes onto the surface of the shell. The structural dynamic equations are coupled to the SVP equations by matching the normal velocity in the fluid to the time derivative of the normal displacement, as well as using the series expansion for surface pressure to form the acoustic contribution to the generalized forces. Results for a spherical shell subjected to a transverse point force at the equator, which is a nonaxisymmetric representation of the excitation, are compared with analytic results. Predictions for a long hemi-capped cylindrical shell in the mid-frequency range are compared to those obtained from SARA-2D (Allik, 1991), which is a finite/infinite element program. In addition to providing validation of the SVP implementation, the cylinder example is used to illustrate the convergence and error measures provided by an SVP analysis.
Frequency Window Implementation of Adaptive Multi-Level Substructuring
Authors: Bennighof J. K. , Kaplan M. F.
Published: February 2008

Adaptive multi-level substructuring (AMLS) is a method for reducing the order of a complex structure’s finite element model by orders of magnitude, while ensuring that the accuracy available from the original model is preserved. A structure’s finite element model is transformed to a much more efficient representation in terms of approximate vibration modes for substructures on multiple levels. An adaptive procedure constructs an optimal model for satisfying a user-specified error tolerance, by determining which modes should be included in the model. In this paper, a frequency window implementation of AMLS is developed, in which frequency response analysis can be done over a frequency window at little additional cost beyond that of the center frequency solution. A numerical example is presented.
Identification of Vibration of Cooler Tubes With Tube-to-Baffle Impacts
Authors: Wong S. C. N. , Chan J. K. T.
Published: February 2008

A random series of impacts method was introduced for vibration test on tube bundles of coolers. A non-normal Poisson process was employed to establish a model for the method. Experimental analysis of the forcing functions showed good agreement with the model. The method was found to be appropriate for extracting modal parameters of such tube structure. Site investigation on power station coolers proved this method to be convenient and reliable. Tube-to-baffle impactions created nonlinear effects which were shown to be of hard-spring type. A piecewise linear system method was used to handle such situation. The theoretical results were closely correlated with the experimental results.
Industrial Noise Source Identification by Using an Acoustic Beamforming System
Authors: Bai M. R. , Lee J.
Published: February 2008

A noise source identification technique is proposed for industrial applications by using a microphone array and beamforming algorithms. Both of the directions and the distances of long-range noise sources are calculated. The conventional method, the minimum variance (MV) method, and the multiple signal classification (MUSIC) method are the main beamforming algorithms employed in this study. The results of numerical simulations and field tests indicate the effectiveness of the acoustic beam-former in identifying noise sources in industrial environments.
Identifying Critical Elastic Scales in Structural-Acoustic Models
Authors: Shepard W. S. , Cunefare K. A. , Ginsberg J. H.
Published: February 2008

The level of detail required for accurate structural acoustic modeling of fluid loaded structures remains an issue of significant debate. Analytical solutions are rarely available, and discrete numerical solutions are typically too complex for ready extraction of physical understanding. In addition, numerical techniques introduce their own explicit scales through the minimum mesh dimension. However, the wavenumber based formulation of the surface variational principle describes the surface pressure and displacement as a comparatively small set of interacting waves. Coupling the SVP with distributed methods of representing structural attachment features provides a means to introduce, control, and investigate features of differing scales. We present here a technique for assessing the critical resolution scales for a fluid loaded two-dimensional plate. For feature attachments, we consider a line-mass elastically suspended by a line-spring from the wetted plate. We then use a spatial expansion for the elastic attachment to the wetted plate. The excitation applied to the plate is taken as a concentrated harmonic force. With the excitation held fixed, the influence of the scale of the feature spatial representation on the radiated power is assessed.
Parametric Instability of a Beam Due to Axial Excitations and to Boundary Conditions
Authors: Dufour R. , Berlioz A.
Published: February 2008

In this paper the stability of the lateral dynamic behavior of a pinned-pinned, clamped-pinned and clamped-clamped beam under axial periodic force or torque is studied. The time-varying parameter equations are derived using the Rayleigh-Ritz method. The stability analysis of the solution is based on Floquet’s theory and investigated in detail. The Rayleigh-Ritz results are compared to those of a finite element modal reduction. It is shown that the lateral instabilities of the beam depend on the forcing frequency, the type of excitation and the boundary conditions. Several experimental tests enable the validation of the numerical results.
Blades Forced Response Analysis With Friction Dampers
Authors: Berthillier M. , Dupont C. , Mondal R. , Barrau J. J.
Published: February 2008

A multiharmonic frequency domain analysis combined with a Craig-Bampton component mode synthesis is presented to compute the dry friction damped forced response of blades. The accuracy of the analysis is established, for a cantilever beam with a dry friction damper attached, by comparison with experimental results and time domain analysis. The method has then been applied to a model fan blade damped by a blade to ground damper.
Nonlinear Vibrations of Elastically-Constrained Rotating Disks
Authors: Yang L. , Hutton S. G.
Published: February 2008

An analysis of nonlinear vibrations of an elastically-constrained rotating disk is developed. The equations of motion, which are two coupled nonlinear partial differential equations corresponding to the transverse force equilibrium and to the deformation compatibility, are first developed by using von Karman thin plate theory. Then the stress function is analytically solved from the compatibility equation by assuming a multi-mode transverse displacement field. Galerkin’s method is applied to transform the force equilibrium equation into a set of coupled nonlinear ordinary differential equations in terms of time functions. Finally, numerical integration is used to solve the time governing equations, and the effects of nonlinearity on the vibrations of a rotating disk are discussed.
Calculating the Time-Histories of Impacting Systems Described by Their Receptances
Authors: Lee C. H. , Byrne K. P.
Published: February 2008

The behavior of impacting systems is highly nonlinear and generally numerical analysis must be resorted to if a quantitative description of the behavior of such systems is required. However, the behaviour of the individual subsystems is often reasonably linear and this along with the fact that the subsystems come into contact when the relative displacements between contact points is zero make it convenient to base the analysis on the receptances, that is, the displacement-force frequency response functions, at the contact points. The procedure for doing this is described with reference to a lumped parameter model. Simple formulae are developed to aid the numerical analysis. The extension of the method to consider continuous systems and those defined by measured receptances is described and examples based on numerically derived and experimentally derived receptances are given.
Calculation of Component Mode Synthesis Matrices From Measured Frequency Response Functions, Part 1: Theory
Authors: Morgan J. A. , Pierre C. , Hulbert G. M.
Published: February 2008

This paper presents a new method to calculate the so-called Craig-Bampton component mode synthesis (CMS) matrices from measured frequency response functions. The procedure is based on a modified residual flexibility method, from which the Craig-Bampton CMS matrices are recovered. Experimental implementation of the method requires estimating the modal parameters corresponding to the measured free boundary modes and the Maclaurin series expansion coefficients corresponding to the omitted modes. Theoretical developments are presented in the present paper, Part 1. The performance of the new method is then demonstrated in Part 2 (Morgan et al., 1998) by comparison of experiment and analysis for a simple two-beam system.
Modeling and Experimental Assessment of Suspension Dynamics of a Horizontal-Axis Washing Machine
Authors: Tu¨rkay O. S. , Su¨mer I. T. , Tugˇcu A. K. , Kiray B.
Published: February 2008

In this paper a nonlinear time variant rigid body dynamic model of the suspension system of an horizontal-axis washing machine is derived using Newton-Euler method, programmed for simulation, and assessed experimentally. The model includes the shock absorbers, the non-linear stiffness of the bellows and also the decoupled spinup motor dynamics. The simulation model predicted the transient and steady-state vertical and horizontal amplitudes of the tub within acceptable errors for a prototype suspension system design. The lift-off and the sliding phenomena of the cabinet have been assessed experimentally using four triaxial piezoelectric force transducers. These were found to be in very good agreement with the theoretical predictions. The model and the simulation code are thus validated experimentally for suspension design optimization of horizontal-axis washing machines.
Rotor Vibration Due to Collision With Annular Guard During Passage Through Critical Speed
Authors: Yanabe S. , Kaneko S. , Kanemitsu Y. , Tomi N. , Sugiyama K.
Published: February 2008

This paper deals with a nonstationary vibration of a rotor due to its collision with a guard during passage through a critical speed. An unbalanced rigid rotor supported by springs and dampers is accelerated at a constant angular acceleration and collides with an annular guard supported by springs and dampers. This dynamic process is calculated by the Runge-Kutta method, and effects of system-parameters on the process are discussed. The collision phenomenon is analyzed through two different theories. In the collision theory, the law of conservation of momentum and the coefficient of restitution are used in order to obtain rotor and guard velocities after collision. The impulse of the force induced by collision is assumed to be equal to the momentum change before and after collision. In the contact force theory, the contact force is assumed to be proportional to the overlapped displacement of the two bodies. Few differences are observed between the calculated responses based on the two theories. In some cases, the rotor executes a diverging backward whirl due to the friction force that occurs during collision with the guard and can not pass through the critical speed. The criteria maps for nonoccurrence of the backward whirl are shown.
High- to Low-Frequency Modal Interactions in a Cantilever Composite Plate
Authors: Oh K. , Nayfeh A. H.
Published: February 2008

We have shown through experiment a complicated dynamic behavior of a cantilever (90/30/–30/–30/30/90)s graphite-epoxy plate. The plate was base excited using a 2000-lb table shaker near its seventh (third torsional) mode. We monitored the input excitation condition using a base mounted accelerometer and the plate response using a laser vibrometer. For some excitation amplitudes and frequencies, we observed the activation of a low-frequency (first bending) mode accompanied by amplitude and phase modulations of the seventh mode. The energy transfer from the high- to low-frequency modes observed in the plate configuration is similar to those observed in flexible beams by Anderson, Balachandran, and Nayfeh (1994) and Nayfeh and Nayfeh (1994) and in frames by Popovic, Nayfeh, Oh, and Nayfeh (1995). Therefore, we conclude that this type of modal interactions is possible for all ranges of structural stiffnesses and configurations whenever there exist modes whose natural frequencies are much lower than the natural frequencies of the directly excited modes. In addition, we also observed simultaneous activation of a two-to-one internal resonance along with the high- to low-frequency modal interactions for some excitation amplitudes and frequencies. We used time-history and power-spectra plots to characterize the experimental data and force-response plots to characterize the dynamics of the plate.
Vibration Analysis of Dry Friction Damped Turbine Blades Using Singular Perturbation Theory
Authors: Ferri A. A. , Heck B. S.
Published: February 2008

The dynamic behavior of a turbine blade with an attached dry friction damper is investigated. Due to the presence of both high and low frequency resonances, the system is numerically stiff and time consuming to simulate. Three reduced-order models that remove the numerical stiffness problem are developed using singular perturbation theory. Two of these models are developed for the case of small damper mass, and the third model is developed for the case of high damper stiffness. It is shown that these models are consistent with two physically-motivated approximate models that have appeared in the literature. The accuracy of each approximate model is examined for a range of system and excitation parameters through comparison with the original full-order model. It is seen that inclusion of damper mass has a significant effect on the blade system response.
Railway Wheel Squeal (Squeal of Disk Subjected to Periodic Excitation)
Authors: Nakai M. , Akiyama S.
Published: February 2008

As a fundamental study of the squeal of a railway wheel running on a corrugated rail, frictional experiments using a thin steel disk and a rod and analysis were performed. A disk representing the railway wheel was clamped at the center with a free periphery and subjected to periodic excitation in its axial direction. When the frequency of excitation is not close to any natural frequency of the disk, squeals with a single nodal diameter mode occur. Squeals at the natural frequency of the disk fall into resonance with the frequency of the excitation, provided that the two frequencies are the same. Then two kinds of squeals occur: squeal at entrained frequency and that at both the entrained frequency and the frequency of another vibrational mode of the disk.
Probability Distribution of Statistical Energy Analysis Model Responses Due to Parameter Randomness
Authors: Huang X. L. , Radcliffe C. J.
Published: February 2008

The Statistical Energy Analysis (SEA) methodology has been widely used in aerospace, ship and automotive industry for high frequency noise analysis and acoustic designs. SEA models are treated here as baseline representations of a population of models for systems such as automotive vehicles. SEA responses from the population of all possible models for a vehicle have a random distribution because of the unavoidable uncertainty in the physical parameters due to fabrication imperfection, manufacturing and assembly variations. The random characteristics of the SEA responses can be described by the response probability distribution. In this work, SEA energy response probability distributions due to parameter randomness in a small neighborhood of nominal design values in frequency bands are proven through the Central Limit Theorem to be Gaussian for infinite number of design parameters. Mean squared sound pressure and velocity are directly proportional to SEA energy responses, their distributions are also shown to be Gaussian. In engineering applications, the number of design parameters is always finite for any SEA models. A Monte Carlo test and Statistical Hypothesis test on a simple 3-element SEA model show that the theoretical, infinite order, Gaussian distributions are good approximations for response distributions of a finite parameter SEA model.
Measurement of Sound Intensity in Comparison With Simulations Using Finite and Semi-infinite Helmholtz Elements
Authors: Giljohann D. , Zopp A.
Published: February 2008

This paper is concerned with the generation and application of semi-infinite Helmholtz elements in accordance with the decay function periodic infinite elements proposed by Bettess (1992). In combination with finite Helmholtz elements, they determine the soundwaves radiated by a vibrating gearbox excited by an impact hammer. The normal velocities on the surface of the gearbox have been measured for a number of different frequencies in order to obtain the dominating frequencies of vibration. Then the velocities of several dominating frequencies are applied as a boundary condition for the simulation of the sound emitted by the structure. The numerical results of the finite element calculations are compared with values obtained by measurement of the sound intensity. It is concluded that semi-infinite Helmholtz elements are as good and as easy to use as measurement techniques in order to identify the zones of main radiation. The deviation of measured and calculated emitted sound power is acceptable.
Required Precision and Valid Methodologies for Dynamic Finite Element Model Updating
Authors: Levin R. I. , Waters T. P. , Lieven N. A. J.
Published: February 2008

This paper investigates the effects of adjusting the system matrices of a Finite Element (FE) model on the eigen-properties of the model for the purposes of dynamic model updating. It is shown that minor modifications to the connectivity of the model can cause unexpectedly significant eigenvalue perturbations of the lower modes, especially if the physical location of the modification is near an antinode of vibration of a lower mode. These modifications can be introduced either by non-parametric updating techniques or unwittingly by truncation of the FE structural matrices. It is proposed that model updating techniques specifically avoid introducing such changes to the model either directly or indirectly. A mathematical bound has been established which gives a limit on eigenvalue perturbations. From this bound it has been deduced that a definable degree of computational precision is necessary for FE analysis for the purposes of model updating.
Vibration of a Cracked Cantilever Beam
Authors: Chondros T. G. , Dimarogonas A. D.
Published: February 2008

A continuous cracked bar vibration model is developed for the lateral vibration of a cracked Euler-Bernoulli cantilevered beam with an edge crack. The Hu-Washizu-Barr variational formulation was used to develop the differential equation and the boundary conditions for the cracked beam as an one-dimensional continuum. The crack was modelled as a continuous flexibility using the displacement field in the vicinity of the crack found with fracture mechanics methods. The results of three independent evaluations of the lowest natural frequency of lateral vibrations of an aluminum cantilever beam with a single-edge crack are presented: the continuous cracked beam vibration model, the lumped crack model vibration analysis, and experimental results. Experimental results fall very close to the values predicted by the continuous crack formulation. Moreover, the continuous cracked beam theory agrees better with the experimental results than the lumped crack flexibility theory.
An Instability Analysis Procedure for Three-Level Multi-Bearing Rotor-Foundation Systems
Authors: Rieger N. F. , Zhou S.
Published: February 2008

A procedure for the instability analysis of three-level multi-span rotor systems is described. This procedure is based on a distributed mass-elastic representation of the rotor system in several eight-coefficient bearings. Each bearing is supported from an elastic foundation on damped, elastic pedestals. The foundation is represented as a general distributed mass-elastic structure on discrete supports, which may have different stiffnesses and damping properties in the horizontal and vertical directions. This system model is suited to studies of instability threshold conditions for multi-rotor turbomachines on either massive or flexible foundations. The instability condition is found by obtaining the eigenvalues of the system determinant, which is obtained by the transfer matrix method from the three-level system model. The stability determinant is solved for the lowest rotational speed at which the system damping becomes zero in the complex eigenvalue, and for the whirl frequency corresponding to the natural frequency of the unstable mode. An efficient algorithm for achieving this is described. Application of this procedure to a rigid rotor in two damped-elastic bearings and flexible supports is described. Application of this procedure to a rigid rotor in two damped-elastic bearings and flexible supports is described. A second example discusses a flexible rotor with four damped-elastic bearings. The third case compares the stability of a six-bearing 300 Mw turbine generator unit, using two different bearing types. These applications validate the computer program and various aspects of the analysis.
Application of Wavelets in Modeling Stochastic Dynamic Systems
Authors: Agrawal O. P.
Published: February 2008

This paper presents a wavelet based model for stochastic dynamic systems. In this model, the state variables and their variations are approximated using truncated linear sums of orthogonal polynomials, and a modified Hamilton’s law of varying action is used to reduce the integral equations representing dynamics of the system to a set of algebraic equations. For deterministic systems, the coefficients of the polynomials are constant, but for stochastic systems, the coefficients are random variables. The external forcing functions are treated as stationary Gaussian processes with specified mean and correlation functions. Using Karhunen-Loeve (K-L) expansion, the random input processes are represented in terms of linear sums of finite number of orthonormal eigenfunctions with uncorrelated random coefficients. A wavelet based technique is used to solve the integral eigenvalue problem. Application of wavelets and K-L expansion reduces the infinite dimensional input force vector to one with finite dimensions. Orthogonal properties of the polynomials and the wavelets are utilized to make the algebraic equations sparse and computationally efficient. A method to compute the mean and the variance functions for the state processes is developed. A single degree of freedom spring-mass-damper system subjected to a random forcing function is considered to show the feasibility and effectiveness of the formulation. Studies show that the results of this formulation agree well with those obtained using other schemes.