bluuebunny/crossref_metadata_2025 huggingface dataset:
A Response Spectrum Method for Seismic Design Evaluation of Rotating Machines
Authors: Singh M. P. , Chang T. S. , Suarez L. E.
Published: June 2008

The equations of motion of rotating machines subjected to seismic motions are quite complex, consisting of asymmetric general matrices with parametric and gyroscopic terms. Fortunately, the parametric and some other terms causing analytical complications can be ignored. This enables one to analyze rotating machines by a generalized modal analysis approach. This approach is used to develop a response spectrum approach for calculating the seismic design response for design inputs defined by response spectrum curves. Applicability of this proposed approach to rotor-bearing systems is verified through a time history ensemble analysis.
Coupled Vibration of Cracked Shafts
Authors: Papadopoulos C. A. , Dimarogonas A. D.
Published: June 2008

The coupling of vibration modes of vibration of a clamped-free circular cross-section Timoshenko beam with a transverse crack is investigated in this paper. A 6 × 6 local flexibility matrix is used to simulate the crack. The nondiagonal terms of this matrix cause coupling between the longitudinal, torsional, and bending vibrations. Coupling is apparent in all spectra obtained with a harmonic sweeping excitation throughout the frequency range. The method is very sensitive even for small cracks.
Theory of Receptance Applied to Modal Analysis of a Spinning Disk With Interior Multi-Point Supports
Authors: Huang S. C. , Hsu B. S.
Published: June 2008

The theory of receptance applied to the modal analysis of a spinning disk with interior multi-point supports is developed. Traveling modes are first introduced for the vibration analysis of a spinning disk. The receptance method is then applied to join the spinning disk and the point supports. The frequency equation and mode shapes are then formulated. An important property, conjugate pairing of the cross receptances is derived. This feature has never been described before in the literature. Numerical results for various numbers of point supports are illustrated. The results show that the nodal pattern of a spinning disk with point supports is varying periodically. The change of rotation speed further causes the mode exchange phenomenon. The change of first critical speed due to point supports is also discussed.
On the Period-Doubling Bifurcations in the Duffing’s Oscillator With Negative Linear Stiffness
Authors: Asfar K. R. , Masoud K. K.
Published: June 2008

The phenomenon of period-doubling bifurcations in the Duffing’s oscillator with negative linear stiffness is investigated with the aid of approximate analytical methods and computer simulation. Making use of a Hill’s type variational equation together with the ideas drawn out from Floquet theory, it is found that a particular type of subharmonic instability is the one that is responsible for the occurrence of period-doublings in this system. This fact is confirmed by the good agreement between the true critical forcing frequency at which bifurcations are first observed, and the one obtained theoretically. Finally, a threshold criterion for the onset of period-doublings is also proposed and compared with computer simulation results.
Spontaneous Sidebanding in High Speed Rotordynamics
Authors: Ehrich F. F.
Published: June 2008

Several observations have been made in the Fourier spectra of high speed rotor-dynamic response of uniformly spaced frequency spikes on either side of key synchronous or subharmonic or superharmonic response frequencies. In instances where this so-called “sidebanding” could not readily be explained as the nonlinear interaction or combination tones of two distinct stimuli at slightly different frequencies, we have referred to this class of phenomena as spontaneous sidebanding. It is invariably noted that the sideband spacing frequency appears to be a whole number fraction (1/J) of the operating speed which suggests that the wave form is periodic and completes a full cycle every J rotations of the rotor. Using a numerical model of a rotor which simulates local contact with a stator in close proximity as a bilinear spring, several studies have been carried out to explore the circumstances for this spontaneous sidebanding. Two general classes of this type of response have been found in systems that are effectively single-degree-of-freedom: (A) For highly nonlinear systems, the chaotic-like response in transition zones between successive orders of subharmonic and superharmonic operation is actually periodic, with a repetition index (J), and results in spontaneous sidebands clustered around the key subharmonic or superharmonic frequencies. No systematic relationship has been determined for the value of (J). (B) In transcritical operation of highly nonlinear and very lightly damped systems, a major sideband frequency spike is noted at a frequency which is approximately the system’s natural frequency. Recognition of this fact permits a simple estimate of the repetition index (J). All these observations from operation of the numerical model have been compared with experimental data derived from incidents of spontaneous sidebanding on aircraft gas turbine rotors. Excellent qualitative agreement has been found in most instances.
Nonlinear Transverse Vibrations and Stability of Spinning Disks With Nonconstant Spinning Rate
Authors: Young T. H.
Published: June 2008

This paper studies nonlinear transverse vibrations of spinning disks with nonconstant spinning rate. Here the angular speed of the disk is characterized as a small, periodic perturbation superimposed upon a constant speed. Due to this perturbation in angular speed, nonautonomous terms appear in the equation of motion, which results in the existence of parametric instability. In this paper, Galerkin’s method is first applied to yield a discretized system, and the method of multiple scales is used to obtain periodic solutions. All types of possible resonant combinations are investigated, and numerical results are shown for a simple harmonic speed perturbation.
The Effect of Close or Repeated Eigenvalues on the Updating of Model Parameters from FRF Data
Authors: Friswell M. I. , Penny J. E. T.
Published: June 2008

Methods to update the parameters of finite element models using measured vibration data usually use the experimentally derived modal model, that is, the system natural frequencies, damping coefficients, and mode shapes. Alternatively the frequency response functions have been used directly to update condensed analytical models and so avoid the sometimes difficult step of deriving the modal model. Previously the authors suggested an algorithm using FRF data that is basically a weighted equation error method based on a reduced order model. This paper investigates the performance of the algorithm for systems with closely coupled or repeated natural frequencies or eigenvalues.
Vibration Confinement Phenomena in Disordered, Mono-Coupled, Multi-Span Beams
Authors: Bouzit D. , Pierre C.
Published: June 2008

The effects of small, periodicity-destroying irregularities on the dynamics of multi-span beams are examined. It is shown that minute deviations of the span lengths from an ideal value alter qualitatively the dynamic response by localizing vibrations and waves to small geometric regions. These confinement phenomena are studied over a wide frequency range for beams resting on simple supports and with variable interspan coupling. Approximations of the localization factor (the average rate of spatial exponential decay of the vibration amplitude) are derived by statistical perturbation methods and validated by Monte Carlo simulations. If the interspan coupling is strong, localization effects are weak and of no practical significance for most engineering structures. On the other hand, localization is severe for small interspan coupling. Confinement is also generally stronger near the edges of frequency passbands and increases nearly linearly with frequency from passband to passband. This means that strong localization occurs at high frequencies, even for large static coupling between spans.
Control of Sound Radiating from an Orthotropic Plate
Authors: Meirovitch L. , Thangjitham S.
Published: June 2008

This paper is concerned with the problem of actively suppressing the acoustic radiation pressure generated by an orthotropic plate vibrating in air. The approach is to control the vibration of the modes of the plate most responsible for acoustic radiation pressure. This is accomplished by relating the far-field radiation pressure to the state of the plate. The control of the far-field radiation pressure is carried out by means of actuators placed on the elastic plate. A numerical example demonstrates the application of active control to suppress the far-field sound radiating from a simply-supported rectangular thin orthotropic plate subjected to a harmonic disturbance. The influence on the control effectiveness of various design parameters, such as the number of controlled modes, the choice of controlled modes, and the number of actuators, is investigated.
On the Burton and Miller Boundary Integral Formulation of the Exterior Acoustic Problem
Authors: Harris P. J. , Amini S.
Published: June 2008

The direct boundary integral equation due to Burton and Miller (1971) is used for the solution of the Helmholtz equation in the exterior domain. The formulation is complex, involving four integral (pseudo-differential) operators. Here we show that it is possible and advantageous to choose the coupling parameter, η, inherent in the formulation, to depend on the boundary points. By setting the coupling parameter, η(p), to zero, over a large part of the surface, we are able to reduce the set up time without greatly affecting the conditioning of the equation.
A Symmetric Inverse Vibration Problem
Authors: Starek L. , Inman D. J. , Kress A.
Published: June 2008

This paper considers the inverse eigenvalue problem for linear vibrating systems described by a vector differential equation with constant coefficient matrices. The inverse problem of interest here is that of determining real symmetric coefficient matrices, assumed to represent the mass, damping, and stiffness matrices, given the natural frequencies and damping ratios of the structure (i.e., the system eigenvalues). The approach presented here allows for repeated eigenvalues, whether simple or not, and for rigid body modes. The method is algorithmic and results in a computer code for determining mass normalized damping, and stiffness matrices for the case that each mode of the system is underdamped.
Hybrid Active Vibration Control of Rotorbearing Systems Using Piezoelectric Actuators
Authors: Palazzolo A. B. , Jagannathan S. , Kascak A. F. , Montague G. T. , Kiraly L. J.
Published: June 2008

The vibrations of a flexible rotor are controlled using piezoelectric actuators. The controller includes active analog components and a hybrid interface with a digital computer. The computer utilizes a grid search algorithm to select feedback gains that minimize a vibration norm at a specific operating speed. These gains are then downloaded as active stiffnesses and dampings with a linear fit throughout the operating speed range to obtain a very effective vibration control.
Design of Shape Memory Alloy Springs With Applications in Vibration Control
Authors: Liang C. , Rogers C. A.
Published: June 2008

Shape memory alloys (SMAs) have several unique characteristics, including their Young’s modulus-temperature relations, shape memory effects, and damping characteristics. The Young’s modulus of the high-temperature austenite of SMAs is about three to four times as large as that of low-temperature martensite. Therefore, a spring made of shape memory alloy can change its spring constant by a factor of three to four. Since a shape memory alloy spring can vary its spring constant, provide recovery stress (shape memory effect), or be designed with a high damping capacity, it may be useful in adaptive vibration control. Some vibration control concepts utilizing the unique characteristics of SMAs will be presented in this paper. Shape memory alloy springs have been used as actuators in many applications although their use in the vibration control area is very recent. Since shape memory alloys differ from conventional alloy materials in many ways, the traditional design approach for springs is not completely suitable for designing SMA springs. Some design approaches based upon linear theory have been proposed for shape memory alloy springs. A more accurate design method for SMA springs based on a new nonlinear thermomechanical constitutive relation of SMA is also presented in this paper.
Timoshenko Beam Modeling for Parameter Estimation of NASA Mini-Mast Truss
Authors: Shen Ji Yao , Huang Jen-Kuang , Taylor L. W.
Published: June 2008

In this paper a distributed parameter model for the estimation of modal characteristics of NASA Mini-Mast truss is proposed. A closed-form solution of the Timoshenko beam equation, for a uniform cantilevered beam with two concentrated masses, is derived so that the procedure and the computational effort for the estimation of modal characteristics are improved. A maximum likelihood estimator for the Timoshenko beam model is also developed. The resulting estimates from test data by using Timoshenko beam model are found to be comparable to those derived from other approaches.
Propagation of Impact-Induced Longitudinal Waves in Mechanical Systems With Variable Kinematic Structure
Authors: Shabana A. A. , Gau W. H.
Published: June 2008

In previous publications by the authors of this paper it was shown that elastic media become dispersive as the result of the coupling between the finite rotation and the elastic deformation. Impact-induced harmonic waves no longer travel, in a rotating rod, with the same phase velocity and consequently the group velocity becomes dependent on the wave number. In this investigation, the propagation of impact-induced longitudinal waves in mechanical systems with variable kinematic structure is examined. The configuration of the mechanical system is identified using two different sets of modes. The first set describes the system configuration before the change in the system topology, while the second set describes the configuration of the system after the topology changes. In the analysis presented in this investigation, it is assumed that collision between the system components occurs first, followed by a change in the system topology. Both events are assumed to occur in a very short-lived interval of time such that the system configuration does not appreciably change. By using the first set of modes, the jump discontinuity in the system velocities is predicted using the algebraic generalized impulse momentum equations. The propagation of the impact-induced wave motion after the change in the system topology is described using the Fourier method. The series solution obtained is used to examine the effect of the topology change on the propagation of longitudinal elastic waves in constrained mechanical systems. It is shown that, while, for a nonrotating rod, mass capture or mass release has no effect on the phase and group velocities, in rotating rods the phase and group velocities depend on the change in the system topology. In particular the phase velocities of low harmonic longitudinal waves are more affected by the change in the system topology as compared to high frequency harmonic waves.
Parametric Identification of a Vibratory System With a Clearance
Authors: Alexander R. M. , Noah S. T. , Franck C. G.
Published: June 2008

An analytical and experimental investigation of a vibratory system with a clearance was conducted. A finite element model and an equivalent single-degree-of-freedom closed-form solution were used to determine the dynamic parameters and response of an experimental structure interacting with a gap. The closed-form solution is obtained by taking advantage of the piecewise linearity of the system. Results from these solution methods are in agreement with experimental data. The results also suggest that the closed-form solution approximates the response of the experimental structure with accuracy greater than that of the finite element model. The closed-form solution was also used to determine the gap size of the structure. The parameter identification procedure utilized in this study appears to be simple to use and can be readily extended to other types of piecewise-linear multi-degree-of-freedom systems.
Sensor Mechanics of Distributed Shell Convolving Sensors Applied to Flexible Rings
Authors: Tzou H. S. , Zhong J. P. , Natori M.
Published: June 2008

Observation spillover can introduce system instability to undamped distributed structural systems. This problem can be prevented via modal filtering using distributed piezoelectric modal sensors which are spatially shaped and convoluted such that they are only sensitive to specific modal mode(s). In this paper, detailed electro-mechanics—sensor mechanics—of spatially distributed piezoelectric shell convolving sensors are analyzed and results presented. It is observed that sensor sensitivity can be classified into two components: (1) the transverse modal sensitivity and (2) the membrane modal sensitivity in which the former is primarily contributed by bending strains and the later is by membrane strains. Design of spatially distributed cosine-shaped convolving sensors for ring structures is proposed and evaluated. Parametric studies suggest that the transverse sensitivity increases and the circumferential sensitivity remained constant when the ring becomes thicker. Both transverse and circumferential sensitivities increase when the piezoelectric layer becomes thicker or with higher piezoelectric constants.
Exact Receptances of Nonproportionally Damped Dynamic Systems
Authors: Yang B.
Published: June 2008

This paper presents an exact method for evaluating the receptances of nonproportionally damped dynamic systems. Based on a decomposition of the damping matrix, an iteration procedure is developed. This method does not require matrix inversion, and completely eliminates the error caused by undamped modal data. Compared to the existing exact solution methods, the proposed method can save more time in the computation. Also, the study yields a convenient way to determine the asymptotic stability of nonproportionally damped systems.
An Experiment on Optimization of Active Noise Control on a Three-Dimensional Extended Radiator
Authors: Giordano J. A. , Cunefare K. A. , Koopmann G. H.
Published: June 2008

In this experiment, a 10.6 dB reduction in the total radiated sound power for an extended radiator was achieved via active control through optimization of active sources. An acoustic boundary element program was used to determine the magnitude and phase of the active sources which minimized the total radiated sound power. This paper details the experimental verification of the numerically predicted active source strengths using a box-shaped acoustic radiator. The top and bottom of the radiator were thin steel plates which were driven in one of their structural modes by an electromagnetic shaker. The four corners of the top plate were removed to accommodate baffled loudspeakers, representing the active sources. To provide precise control of the experiment, the driving signals to the shakers and loudspeakers were generated and monitored by a control computer. The experimental results agreed closely with the analytical prediction, confirming that the optimum reduction had been achieved for the primary and active source configuration. The measured sound pressure reductions in the acoustic field of the radiator ranged from 8 dB to 19 dB for the 1,1 structural mode of the plates.
Stochastic Finite Element Analysis for High Speed Rotors
Authors: Sankar T. S. , Ramu S. A. , Ganesan R.
Published: June 2008

The general problem of the dynamic response of highspeed rotors is considered in which certain system parameters may have a spatial stochastic variation. In particular the elastic modulus and mass density of a rotating shaft are described through one dimensional stochastic field functions so that the imperfections in manufacture and measurement can be accounted for. The stochastic finite element method is developed so that the variability of the response of the rotor can be interpreted in terms of the variation of the material property. As an illustration the whirl speed analysis is performed to determine the stochastics of whirl speeds and modes through the solution of a random eigenvalue problem associated with a non self-adjoint system. Numerical results are also presented.
Response of a Stationary, Damped, Circular Plate Under a Rotating Slider Bearing System
Authors: Shen I. Y.
Published: June 2008

This paper is to demonstrate that axisymmetric plate damping will suppress unbounded response of a stationary, elastic, circular plate excited by a rotating slider. Use of the method of multiple scales shows that the axisymmetric plate damping will suppress parametric resonances excited by slider stiffness and slider inertia at supercritical speed. In addition, the plate damping will increase the onset speed above which slider damping destabilizes the elastic circular plate. Moreover, numerical examples show that the plate damping could stabilize the plate/slider system at discrete rotation speeds above the onset speed.
Large Amplitude Free Vibration of Shallow Spherical Shell on a Pasternak Foundation
Authors: Paliwal D. N. , Bhalla V.
Published: June 2008

Large amplitude free vibrations of a clamped shallow spherical shell on a Pasternak foundation are studied using a new approach by Banerjee, Datta, and Sinharay. Numerical results are obtained for movable as well as immovable clamped edges. The effects of geometric, material, and foundation parameters on relation between nondimensional frequency and amplitude have been investigated and plotted.
The Residual Variable Method Applied to Acoustic Wave Propagation from a Spherical Surface
Authors: Akkas N. , Erdogan F.
Published: June 2008

The classical wave equation in spherical coordinates is expressed in terms of a residual potential applying the Residual Variable Method. This method essentially eliminates the second derivative of the potential with respect to the radial coordinate from the wave equation. Thus, the dynamic pressure distribution on the surface of a spherical cavity can be studied by considering the cavity surface only. Moreover, the Residual Variable Method, being amenable to “marching” solutions in a finite-difference implementation, is very suitable for the analysis of acoustic wave propagation into the finite medium from the cavity surface. The propagation of the wave from the internal surface can be followed numerically. There is no need to discretize the infinite domain in its entirety at all. The propagation analysis can be terminated at any point in the radial direction without having to consider the rest.
Analysis of Dynamic Systems With Periodically Varying Parameters Via Chebyshev Polynomials
Authors: Sinha S. C. , Wu Der-Ho , Juneja V. , Joseph P.
Published: June 2008

In this paper a general method for the analysis of multidimensional second-order dynamic systems with periodically varying parameters is presented. The state vector and the periodic matrices appearing in the equations are expanded in Chebyshev polynomials over the principal period and the original differential problem is reduced to a set of linear algebraic equations. The technique is suitable for constructing either numerical or approximate analytical solutions. As an illustrative example, approximate analytical expressions for the Floquet characteristic exponents of Mathieu’s equation are obtained. Stability charts are drawn to compare the results of the proposed method with those obtained by Runge-Kutta and perturbation methods. Numerical solutions for the flap-lag motion of a three-bladed helicopter rotor are constructed in the next example. The numerical accuracy and efficiency of the proposed technique is compared with standard numerical codes based on Runge-Kutta, Adams-Moulton, and Gear algorithms. The results obtained in both the examples indicate that the suggested approach is extremely accurate and is by far the most efficient one.
Dynamic Response of an Axially Moving Beam Coupled to Hydrodynamic Bearings
Authors: Tan C. A. , Yang B. , Mote C. D.
Published: June 2008

The vibration response of a distributed axially moving beam, controlled through distributed hydrodynamic bearing forces, is analyzed by the transfer function method. In the axially moving beam, all modes are affected by the distributed bearing coupling. The bearing force is described in terms of impedance functions. An approximate closed-form transfer function for the coupled beam-bearing system is derived. The transfer function is applicable to all linear, one-dimensional, coupled systems, and it is exact for localized, linear constraint forces. The derivation requires knowledge of the transfer function of the axially moving beam which is not available in the literature. A method for determining the beam transfer function is also presented. The frequency response of the coupled system is illustrated for several beam and bearing design parameters.
Rotor Whirl Measurements on a Long Rotating Cylinder Partially Filled With Liquid
Authors: Colding-Jo̸rgensen J.
Published: June 2008

A theoretical analysis of a long flexibly suspended, rotating cylinder partially filled with liquid has been presented earlier (Colding-Jo̸rgensen, 1990). Special emphasis has been placed on dynamic stability, application in centrifuges, and the influence of external damping. The present paper presents experimental results for comparison with the theoretical analysis, especially in regard to unstable speed ranges, whirl speed relative to rotational speed, and limit cycle amplitudes with external damping. The theory agrees quantitatively with regard to speed ranges and whirl frequency ratios but only qualitatively with regard to whirl amplitudes, indicating the need for further development of the nonlinear analysis of the fluid motion with external damping.
Free Linear Vibration of Self-Pressurized Foil Bearings
Authors: Wickert J. A.
Published: June 2008

A foil bearing is formed when a flexible medium travels across a stationary rigid surface and entrains a thin layer of fluid that lubricates the relative sliding motion. Such bearings are used in magnetic tape drives to prevent excessive wear of the recording head and tape interface. In the one-dimensional model considered here, the tape is approximated as an axially-moving Euler-Bernoulli beam under tension, and the air pressure in the bearing region satisfies Reynolds equation for unsteady compressible flow. To the extent that transverse deformation of the tape couples with the air pressure, the “foil bearing problem” falls within the discipline of elastohydrodynamic lubrication. The governing equations for the tape and recording head are linearized about the equilibrium displacement and pressure fields, and the two resulting coupled partial differential equations with nonconstant coefficients describe the linear response. Following global discretization through Galerkin’s method, the natural frequencies, damping, and mode shapes of the tape and recording head system are determined through numerical solution of the generalized matrix eigenvalue problem. The coupled displacement and pressure modes depend on the transport speed, and they are complex because of viscous dissipation of the air and convection of the tape. For the illustrative case of a semicircular recording head, the dependence of the system’s eigenvalues on the transport speed, and on the location of the recording head within the tape’s span, is discussed.
Vibration of a Spinning Annular Disk With Coupled Rigid-Body Motion
Authors: Yang Shih-Ming
Published: June 2008

The vibration of a spinning annular disk with coupled translational and rotational rigid-body motion is analyzed. The spinning disk, with one linear spring as transverse load, is free to translate and rotate relative to the shaft axis. Modal functions of a stationary annular disk are used to describe the elastic displacement of the spinning disk. The governing equation includes the rigid disk translation, rotation, and the flexible disk vibration. Coupling effects between the rigid-body motion and the annular disk modal function are identified in the formulation. Because of the coupling effects, stable operation beyond divergence (critical speed) is achieved, the disk loses its stability to flutter. This stability prediction is different from that of a spinning disk without rigid-body motion where the disk is unstable at and right after divergence.
Modal Testing Theory of Rotor-Bearing Systems
Authors: Jei Yang-Gyu , Kim Young-Ju
Published: June 2008

Since all dynamic characteristics of rotor systems are closely related with rotor rotations, the directivity of modes is very important in rotor dynamics. But the classical modal testing theories which have been applied to nonrotating structures were often applied to rotor systems. Whereas the dynamic characteristics in negative frequency region have no meanings in nonrotating stuctures, the dynamic characteristics of rotor systems in the negative frequency region which are different from those in the positive frequency region have significant physical meanings. Here a new modal testing theory is proposed to separate the rotor vibration into positive and negative frequency regions. In particular, the amplitude and directivity variations of frequency response functions in positive and negative frequency regions are discussed when using complex modal displacement. And a method to identify the directivity of modes such as forward and backward is suggested using the frequency response function obtained by the proposed modal testing theory. The whirl directions of forced responses related with the directivity of modes are also discussed. In addition, even if the anisotropy in bearings and the effects of gyroscopic moments are permitted, the relations between the right and left eigenvectors of general damped anisotropic rotor systems are evaluated under some practical conditions. If the relations between the right and left eigenvectors are given, the necessity of additional modal testing to identify the adjoint modal parameters is relaxed.
Structural Modal Multifurcation With International Resonance: Part 1—Deterministic Approach
Authors: Ibrahim R. A. , Afaneh A. A. , Lee B. H.
Published: June 2008

The bifurcation and multifurcation in multimode interaction of nonlinear continuous structural systems is investigated. Under harmonic excitation the nonstationary response of multimode interaction is considered in the neighborhood of fourth-order internal resonance condition. The response dynamic characteristics are examined via three different approaches. These are the multiple scales method, numerical simulation, and experimental testing. The model considered is a clamped-clamped beam with initial static axial load. Under certain values of the static load the first three normal modes are nonlinearly coupled and this coupling results in a fourth-order internal resonance. The method of multiple time scales yields nonstationary response in the neighborhood of internal resonance. Within a small range of internal detuning parameter the third mode, which is externally excited, is found to transfer energy to the first two modes. Outside this region, the response is governed by a unimodal response of the third mode which follows the Duffing oscillator characteristics. The bifurcation diagram which represents the boundaries that separate unimodal and mixed mode responses is obtained in terms of the excitation level, damping ratios, and internal resonance detuning parameter. The domains of attraction of the two response regimes are also obtained. The numerical simulation of the original equations of motion suggested the occurrence of complex response characteristics for certain values of damping ratios and excitation amplitude. Both numerical integration and experimental results reveal the occurrence of multifurcation as reflected by multi-maxima of the response probability density curves.
Natural Frequencies and Mode Shapes of Beams Carrying a Two Degree-of-Freedom Spring-Mass System
Authors: Jen Ming Une , Magrab E. B.
Published: June 2008

An exact solution for the natural frequencies and mode shapes for a beam elastically constrained at its ends and to which a rigid mass is elastically mounted is obtained. The attached mass can both translate and rotate. The general solution is obtained using the Laplace transform with respect to the spatial variable and yields the exact solutions to several previously published simpler configurations that were obtained using approximate methods. Numerous numerical results are presented for the natural frequency coefficients that extend previously reported results and that show the transition between various limiting cases. In addition, values are presented for the lowest two natural frequency coefficients for a beam that is clamped at both ends and is carrying a two dof spring-mass system. Representative mode shapes at selected values of the system’s parameters are also given.
Optimal Design of Centered Squeeze Film Dampers
Authors: Nataraj C. , Ashrafiuon H.
Published: June 2008

A two degree-of-freedom model, consisting of a rigid rotor supported on rigid bearings which are in turn supported on squeeze film dampers, is considered. Isotropic centering springs are assumed resulting in a steady synchronous centered circular response for the rotor. The resulting nonlinear system is modeled in nondimensional form. The transmissibility ratio of the system as well as the power dissipated are minimized for various values of unbalance and at several speeds, with the squeeze film bearing parameter as the primary design variable. Expressions are derived for linear variational stability of the circular orbit, and are imposed as constraints in the optimization process. The dependence of the optimal configuration on speed and unbalance is discussed.
Noise Reduction of Pressure Type Fans for Automobile Air Conditioners
Authors: Akaike S. , Kikuyama K.
Published: June 2008

Automotive air conditioners often employ a pusher-type condenser cooling system. Because the axial fan in such cooling systems is a major source of noise in the engine compartment, much effort has been directed to reducing the noise emitted by the fan. This paper clarifies the mechanism by which the fan of a pusher-type cooling system generates noise and presents ways to decrease the turbulent noise from it. Detailed studies of the flow around the fan were made using computer simulations and LDA (Laser Doppler Anemometer) measurements. A considerable reduction in the noise level of pusher-type cooling system has been achieved for different resistances without any deterioration in performance.
Vibration Response Reduction of a Rotor Shaft System Using Viscoelastic Polymeric Supports
Authors: Dutt J. K. , Nakra B. C.
Published: June 2008

The main objective of the present work is to determine reduction in the unbalance response of a rotor shaft system by using a suitable polymeric or viscoelastic bearing support. For analysis, a simple rotor system has been taken with the rotor placed in the middle of a massless shaft with linear elastic bearings at the ends, having viscoelastic supports. A procedure is given for determining the frequency dependence of viscoelastic support characteristics so that the frequency of excitation never coincides with any of the undamped natural frequencies of the system, thus giving low unbalance response over a wide frequency range and the support material can be chosen accordingly.
Spatial Domain Modal Analysis of Lightly-Damped Structures Using Laser Velocimeters
Authors: Arruda J. R. F.
Published: June 2008

Traditional modal identification techniques do not take advantage of the high spatial density of scanning Laser Doppler Velocimeter (LDV) measurements. In this paper, a spatial modal parameter estimation technique, specially adapted for use with LDV measurements, is presented. It is based on a real-mode modal filtering concept and, therefore, is applicable to structures with low damping. From the estimated mode shape surfaces, curve-fitted with two-dimensional Fourier series, angular displacements are calculated. A rectangular plate example illustrates the proposed techniques with both numerically simulated and experimental results.
Experimental and Numerical Analysis of Bimodal Acoustic Agglomeration
Authors: Hoffmann T. L. , Chen W. , Koopmann G. H. , Scaroni A. W. , Song L.
Published: June 2008

The interaction between fly ash particles (first mode) and sorbent particles (second mode) in coal combustion processes is studied under the influence of a low frequency, high intensity acoustic field. The effect of bimodal acoustic agglomeration is evaluated in a numerical sensitivity analysis on parameters such as residence time in the combustion chamber and mass loading of the particle modes. An Acoustic Agglomeration Simulation Model (AASM) developed by Song at the Pennsylvania State University is used for these numerical studies. Experimental examinations carried out in a down-fired combustor show evidence of bimodal agglomeration and enhanced particle interaction under the influence of a low frequency (44 Hz), high intensity (160 dB) sound field. The results of the experiments are compared to the equivalent numerical studies and good agreement can be shown between the two sets of data.
Vibration on an Inclined Rotating Cantilever Beam With Tip Mass
Authors: Lee Heow-Pueh
Published: June 2008

The vibration of a rotating cantilever beam with a tip mass is studied with the configuration of the undeformed beam deviating from the radial direction at the clamped end. The equation of motion is formulated based on the Hamilton’s principle and then reduced to the form of a matrix eigenvalue problem for constant rotational speed of the hub. The results of numerical simulations are compared with results from various authors using finite element, Rayleigh-Ritz, and Myklestad methods. The variation of natural frequency with rotational speed of the hub is then presented for various combinations of hub radius, tip mass, and angle of deviation of the undeformed beam from the radial direction.
Derivatives of Eigenvalues for Torsional Vibration of Geared Shaft Systems
Authors: Zhong-Sheng Liu , Su-Huan Chen , Tao Xu
Published: June 2008

Design sensitivity analysis of natural frequency for geared shaft systems is of practical importance in the optimal design of these systems. This note provides a simple and easily implemented method to calculate the eigenvalue derivatives of a geared shaft system with respect to a design parameter ν, including gear inertia J, shaft stiffness K, and transmission ratio Q, when the eigensolution is known. An example is given to illustrate the method.
The Rayleigh-Ritz Method With Quasi-Comparison Functions in Nonself-Adjoint Problems
Authors: Hagedorn P.
Published: June 2008

In the determination of the first eigenmodes of continuous linear elastic systems the Rayleigh-Ritz method is often used. It is also very useful in the discretization of the elastic members of multibody systems undergoing large nonlinear motions. Recently the concept of quasi-comparison functions has been introduced for the Rayleigh-Ritz discretization in self-adjoint eigenvalue problems, where it may lead to a considerable improvement of the convergence when compared with other classes of admissible functions. In this paper it is shown with a simple example that a similar phenomenon also holds for nonself-adjoint problems. Since the exact solutions are known, precise information on the errors can be given.
Transverse Vibrations of a Rotating Twisted Timoshenko Beam Under Axial Loading
Authors: Chen W.-R. , Keer L. M.
Published: June 2008

Transverse bending vibrations of a rotating twisted beam subjected to an axial load and spinning about its axial axis are established by using the Timoshenko beam theory and applying Hamilton’s Principle. The equations of motion of the twisted beam are derived in the twist nonorthogonal coordinate system. The finite element method is employed to discretize the equations of motion into time-dependent ordinary differential equations that have gyroscopic terms. A symmetric general eigenvalue problem is formulated and used to study the influence of the twist angle, rotational speed, and axial force on the natural frequencies of Timoshenko beams. The present model is useful for the parametric studies to understand better the various dynamic aspects of the beam structure affecting its vibration behavior.
Transverse Vibration of Plate Structures With Elastically Restrained Edges by the Spline/Finite Strip Method
Authors: Sheikh Abdul Hamid , Mukhopadhyay Madhujit
Published: June 2008

The newly developed spline finite strip method has been applied to determine the natural frequencies of plates and stiffened plates with edged elastically restrained against translation and rotation. The stiffener has been modelled so that it can be situated anywhere within the plate strip. The formulation has been generalized in such a manner that it can handle general shaped plates and stiffeners having arbitrary orientation and eccentricity. A consistent formulation has been adopted to incorporate the contribution of the edge restraints in the structural stiffness matrix. Numerical examples as available in the literature are solved and the comparison of the results indicates good accuracy of the method. New results in the form of natural frequencies corresponding to the higher modes particularly for plates/stiffened plates with nonclassical boundaries are presented.
Stability Boundary of Non-Linear Orbits Within Clearance Circle of Journal Bearings
Authors: Khonsari M. M. , Chang Y. J.
Published: June 2008

The transient, nonlinear study of journal bearing stability requires tracking the locus of the shaft center as a function of time. It is shown that there exists a boundary within the bearing clearance circle outside of which any initial condition would yield an unstable orbit. This is shown to be the case for operating speeds that are well below the threshold of instability according to the linearized stability analysis.
An Extending Dynamic Elastica: Impact With a Surface
Authors: Stolte J. , Benson R. C.
Published: June 2008

The study of the dynamic transport of paper, film, and tape is of increasing importance as process speeds increase. In earlier machines, transport velocities were slow enough that inertia loads did not appreciably affect the deformation of the material. In many applications, material is pushed from a channel or clamp and can be modeled as a cantilevered beam or plate until it reaches another guide or barrier. In this paper, we are concerned with modeling the behavior of such a cantilevered sheet after it strikes a guide. The guide may be any two-dimensional curve. We are able to determine leading edge velocities and reaction forces necessary to keep the sheet from penetrating the guide. Friction is included in the model. The sheet is allowed to exit the channel at an arbitrary angle and may have a nonconstant transport velocity. Inertial loads become noticeable at speeds greater than one copy per second and are necessary for the resolution of impact loads.
Modal Element Method for Scattering and Absorbing of Sound by Two-Dimensional Bodies
Authors: Baumeister K. J. , Kreider K. L.
Published: June 2008

The modal element method for acoustic scattering from a two-dimensional body is presented. The body may be acoustically soft (absorbing) or hard (reflecting). The infinite computational region is divided into two subdomains—the bounded finite element domain, which is characterized by complicated geometry and/or variable material properties, and the surrounding unbounded homogeneous domain. The acoustic pressure field is represented approximately in the finite element domain by a finite element solution, and is represented analytically by an eigenfunction expansion in the homogeneous domain. The two solutions are coupled by the continuity of pressure and velocity across the interface between the two subdomains. Also, for hard bodies, a compact modal ring grid system is introduced for which computing requirements are drastically reduced. In this paper, analysis for two-dimensional scattering from solid and coated (acoustically treated) bodies is presented, and several simple numerical examples are discussed. In addition, criteria are presented for determining the number of modes to accurately resolve the scattered pressure field from a solid cylinder as a function of the frequency of the incoming wave and the radius of the cylinder.
Extended Kirchhoff Integral Formulations for Sound Radiation from Vibrating Cylinders in Motion
Authors: Wu S. F. , Wang Z.
Published: June 2008

This paper presents numerical results of sound radiation from vibrating cylinders in rectilinear motion at constant subsonic speeds by using the extended Kirchhoff integral formulations recently derived by Wu and Akay (1992). In particular, the effects of the interaction between the turbulent stress field and the vibrating surface in motion are examined. Numerical results demonstrate that this interaction is significant in the near-field when the dimensionless frequency ka > 2 and the dimensionless source translational speed M > 0.1. If this interaction is completely neglected, the predicted acoustic pressure is underestimated by as much as 10 to 20 percent in the near field. The effects of this interaction, however, decrease in the far-field. The effects of surface translational motion on the resulting sound radiation are also examined. It is found that the surface translational motion has a significant effect on the resulting sound generation in both near- and far-fields. The amplitude of the acoustic pressure is approximately doubled in the forward direction when ka > 2 and M > 0.2, which corresponds to at least a 5 dB increase in the SPL value.
Piezoelectric Actuators for Distributed Vibration Excitation of Thin Plates: A Comparison Between Theory and Experiment
Authors: Clark R. L. , Flemming M. R. , Fuller C. R.
Published: June 2008

Experimental results from vibration excitation of a simply supported plate with multiple patches of piezoceramic material bonded to the surface are compared to theoretical predictions for the vibration response. Results demonstrate that modes can be selectively excited depending on the chosen phasing of the voltage supplied to each actuator. In addition, experimental results indicate that the analytical model can be accurately used to predict the forcing function associated with the piezoceramic patch.
On the Occurrence of Simultaneous Resonances in Parametrically-Excited Rectangular Plates
Authors: Ostiguy G. L. , Samson L. P. , Nguyen H.
Published: June 2008

The present work deals primarily with the problem of the occurrence of simultaneous resonances in parametrically-excited rectangular plates. The analysis is based on the dynamic analog of the von Karman’s large-deflection theory and the governing equations are satisfied using the orthogonality properties of the assumed functions. The temporal response of the damped system is determined by the generalized asymptotic method and various types of simultaneous resonances are investigated. An experimental investigation is performed to verify the analytical predictions and to possibly discover new phenomena not predicted by the theory. Experiments are conducted for four different sets of boundary conditions. Analytically defined simultaneous resonances are experimentally observed and isolated.