bluuebunny/crossref_metadata_2025 huggingface dataset:
Design of Magnetic Bearings for Rotor Systems With Harmonic Excitations
Authors: Dhar D. , Barrett L. E.
Published: June 2008

This paper presents a method for calculating the control forces and the bearing stiffness and damping coefficients to control the response of multi-mass flexible rotor systems mounted on magnetic bearings and subjected to unbalance or harmonic excitation forces. The capability for inclusion of hydrodynamic bearings is retained to model seal effects or to permit the design of magnetic bearings for hybrid systems. Control forces at the magnetic bearing locations are evaluated based on the desired shaft response specified by the modal coordinates. These forces are determined such that the error between the desired response and the achieved response is minimized in a least-square sense. Equivalent bearing coefficients are calculated from the control forces and the achieved response which when superimposed on the nominal bearing coefficients yield the resultant magnetic bearing coefficients required for control. An example case is presented where control of rotor response has been attempted at the first and the second unbalance critical speeds. The results demonstrate appreciable improvement in response using magnetic bearings.
Dynamic Behavior of Valves with Pneumatic Chambers for Reciprocating Compressors
Authors: Kato M. , Kurohashi M. , Aoshima M.
Published: June 2008

This paper describes the dynamic behavior of valves with pneumatic chambers for reciprocating compressors. These are known as “damped valves” and are capable of reducing the impact on the valve seat and valve stopper. The characteristics of the dynamic behavior of the damped valves were clarified by calculating newly derived governing equations of valve dynamics. From the calculated results, it becomes apparent that the volume of the pneumatic chambers and the clearance between the pneumatic chamber and the valve have a large influence on the impact speed of the valves. Furthermore, the valves tend to close later for a higher compressor speed to oscillate at a larger amplitude for a lower density of gas such as hydrogen. These tendencies show that the selection of the specification of damped valves is very important. The stiffness of the valve spring and the lift of the valve also affect valve behavior as with valves without pneumatic chambers.
Optimum Design of Optical Pick-Up by Elimination of Resonance Peaks
Authors: Kajiwara I. , Nagamatsu A.
Published: June 2008

A method for structural dynamic optimization is proposed using sensitivity analysis of resonance and anti-resonance frequencies. The sensitivity of the anti-resonance frequency is newly defined. An approach for eliminating the resonance peak from the frequency response function (FRF) is proposed using this sensitivity, modifying both the frequencies of this resonance and the neighboring anti-resonance bottom to the same value. The proposed method is applied to determine the optimum thickness of a plate in order to eliminate resonance peaks from its FRF. Effectiveness of this method is verified experimentally. Optimum design of an optical actuator for a compact disk player is performed practically by eliminating resonance peaks which deteriorates its servo control function. The player, with this optimized actuator, shows an excellent performance of sound playback.
Waves on Fluid-Loaded Inhomogeneous Elastic Shells of Arbitrary Shape
Authors: Pierce A. D.
Published: June 2008

A generalization of the Donnell model for a thin shell of arbitrary shape, and with position-dependent elastic and geometric properties, is used to formulate a wave theory for quasi-straight-crested waves of constant frequency propagating over the shell’s surface. The principal restriction on the theory is that the wavenumber components must be large compared with the two principal curvatures. A simple method for including fluid loading in the model yields a finite local specific radiation impedance even when the waves on the surface are moving with the fluid’s sound speed. The overall model is then used to derive a general dispersion relation which connects frequency and wavenumber components for the fundamental waves of the fluid-shell system.
Experimental and Analytical Study of the Frequencies of an S-C-S-C Plate Carrying a Concentrated Mass
Authors: Low K. H. , Chai G. B. , Ng C. K.
Published: June 2008

The present work is concerned with the determination of the fundamental frequencies of a simply supported-clamped-simply supported-clamped (SCSC) plate carrying a concentrated mass. An energy method based on the Rayleigh’s approach has been developed to obtain approximate closed-form solutions. A finite element analysis is also presented for comparison. Extensive experimental investigation through a shaker system was conducted to collect useful test data. The comparison of experimental results with theoretical predictions of the energy method shows favorable correlations. In the parametric study, the effect of various sizes of the concentrated mass, and the effect of the variation in the plate geometry and material properties on the fundamental frequencies of the plate are presented.
Mode Superposition Analysis of Viscously Damped Nonlinear Structural Systems Using an Incremental Algorithm
Authors: Lin Yang-Tai , Sun Te-Chang
Published: June 2008

A mode superposition method for approximately solving the dynamic response of viscously damped nonlinear structural systems is presented, which is characterized by high accuracy and low computational cost. The method is based on an incremental decomposition procedure to formulate the motion of the discrete system, which is established by finite element theory for spatial dependence and both geometric and material nonlinearities are considered. The accuracy and efficiency are studied through two practical problems. By comparing the results using the present method with those using the direct time integration, it is found that the error is negligible and the computational effort can be significantly reduced.
On the Symmetrization of Asymmetric Finite Dimensional Linear Dynamic Systems
Authors: Cherng An-Pan , Abdelhamid M. K.
Published: June 2008

A linear dynamic system with constant mass, and asymmetric damping and stiffness coefficient matrices, may be transformed to a symmetric system where all coefficient matrices are symmetric. This transformation makes it possible to take advantage of the well-developed theories that use the properties of the symmetric coefficient matrices. Some previous studies have suggested a decomposition method associated with rank checking of a rectangular matrix to determine if such transformations exist. However, these methods were only applicable to coefficient matrices with distinct eigenvalues, and they are computationally intensive. In this paper, a general discussion of the symmetrization problem is presented. A new method for assessing the symmetrizability and a way to find one of such transformations (if they exist) is also proposed. The method needs a fraction of the computations needed for published methods. The proposed method is tailored to treat coefficient matrices with repeated eigenvalues as well as distinct eigenvalues. Four examples, of which three are from previous studies, are used to demonstrate the proposed method. The results show that the proposed method is more computationally efficient than previously published methods, and accommodates the repeated eigenvalue problem.
Unbalance Response of a Dual Rotor System: Theory and Experiment
Authors: Gupta K. , Gupta K. D. , Athre K.
Published: June 2008

A dual rotor rig is developed and is briefly discussed. The rig is capable of simulating dynamically the two spool aeroengine, though it does not physically resemble the actual aeroengine configuration. Critical speeds, mode shape, and unbalance response are determined experimentally. An extended transfer matrix procedure in complex variables is developed for obtaining unbalance response of dual rotor system. Experimental results obtained are compared with theoretical results and are found to be in reasonable agreement.
Two-Channel Laser Vibrometer Techniques for Vibrational Intensity Measurements: Part 1—Flexural Intensity
Authors: McDevitt T. E. , Koopmann G. H. , Burroughs C. B.
Published: June 2008

A laser technique which measures vibrational energy flow (intensity) via propagating bending waves is described. A pair of scanning laser beams from a two-channel laser vibrometer is used to provide a nonintrusive measurement of the intensity at various points on a vibrating beam. Results are shown to compare well with those of two additional techniques. These techniques, used for validation, employ a single laser beam and can only be used at resonance frequencies in beams or rods. The two-channel laser technique described can be applied to two-dimensional intensity measurements, is not limited to single frequency excitation, and has an inherent capability to facilitate phase error elimination via a photodetector switching technique which is also described.
Flexural Vibration of In-Plane Loaded Plates with Straight Line/Curved Internal Supports
Authors: Liew K. M. , Wang C. M.
Published: June 2008

An investigation into the vibration analysis of a class of in-plane loaded rectangular plates with internal supports of arbitrary contour is conducted. Solutions to this vibration problem are obtained based on the pb-2 Rayleigh-Ritz method. The Ritz function for this method is defined as the product of (1) a two-dimensional polynomial function expanded in a new manner, (2) equations of the internal support and (3) equations of the boundary supports each raised to the power of either 0, 1, or 2 corresponding to a free, simply supported or clamped edge, respectively. A comparison study on the convergence between the proposed set of polynomials and mathematically complete set of polynomials is conducted. The simplicity and accuracy of the method are demonstrated by analyzing square plates with either two intersecting internal line supports or a central ring support. The influence of the in-plane loads on the natural frequencies will be studied. Note that this paper presents some first known solutions to in-plane loaded rectangular plates with internal supports of arbitrary contour. The mode shapes for these plates are also presented in contour plots.
Numerical Approach to Far Field Acoustic Wave Propagation from a Prolate Spheroidal Surface
Authors: Wright J. P.
Published: June 2008

A method is described for calculating the far field, transient, three-dimensional pressure field generated by acoustic waves emanating from a prolate spheroidal surface. The pressure field is expanded in a series of spherical harmonics, which leads to a system of linear, tridiagonal, one dimensional wave equations that can be integrated efficiently by numerical techniques based on the method of characteristics. Integrals involving orthogonal functions are approximated by a numerically robust scheme where exact orthogonality is obtained (in the absence of round-off errors) in terms of weighted sums over a discrete variable.
Design Optimization of Aircraft Engine-Mount Systems
Authors: Ashrafiuon H.
Published: June 2008

Design optimization of aircraft engine-mount systems for vibration isolation is presented. The engine is modeled as a rigid body connected to a flexible base representing the nacelle. The base (nacelle) is modeled with mass and stiffness matrices and structural damping using finite element modeling. The mounts are modeled as three-dimensional springs with hysteresis damping. The objective is to select the stiffness coefficients and orientation angles of the individual mounts in order to minimize the transmitted forces from the engine to the nacelle. Meanwhile, the mounts have to be stiff enough not to allow the engine deflection to exceed its limits under static and low frequency loadings. It is shown that with an optimal system the transmitted forces may be reduced significantly particularly when orientation angles are also treated as design variables. The optimization problems are solved using a constraint variable metric approach. The closed form derivatives of the engine vibrational amplitudes with respect to design variables are derived in order to determine the objective function gradients and consequently a more effective optimization search technique.
Forced Vibration of Flexible Body Systems: A Dynamic Stiffness Method
Authors: Liu T. S. , Lin J. C.
Published: June 2008

Due to the development of high speed machinery, robots, and aerospace structures, the research of flexible body systems undergoing both gross motion and elastic deformation has seen increasing importance. The finite element method and modal analysis are often used in formulating equations of motion for dynamic analysis of the systems which entail time domain, forced vibration analysis. This study develops a new method based on dynamic stiffness to investigate forced vibration of flexible body systems. In contrast to the conventional finite element method, shape functions and stiffness matrices used in this study are derived from equations of motion for continuum beams. Hence, the resulting shape functions are named as dynamic shape functions. By applying the dynamic shape functions, the mass and stiffness matrices of a beam element are derived. The virtual work principle is employed to formulate equations of motion. Not only the coupling of gross motion and elastic deformation, but also the stiffening effect of axial forces is taken into account. Simulation results of a cantilever beam, a rotating beam, and a slider crank mechanism are compared with the literature to verify the proposed method.
Vibration Isolation in a Microgravity Environment
Authors: Alexander R. M. , Gerhold C. H. , Atwood C. B. , Cordera J. F.
Published: June 2008

Many in-space research experiments require the microgravity environment attainable near the center of mass of the proposed space station. Since dynamic disturbances to the surrounding structure may undermine an experiment’s validity, isolation of these experiments is imperative. This paper summarizes analytical and experimental work accomplished to develop an isolation system which allows the pay load to float freely within a prescribed boundary while being kept centered with forces generated by small jets of air. An experimental setup was designed and constructed to simulate the microgravity environment In the horizontal plane. Results demonstrate the air jet control system to be effective in managing payload oscillatory response. An analytical model was developed and verified by comparing predicted and measured payload response. The mathematical model is then used to investigate payload response to disturbances likely to be present in the space station.
Modeling Rotating Shafts Using Axisymmetric Solid Finite Elements with Matrix Reduction
Authors: Stephenson R. W. , Rouch K. E.
Published: June 2008

An axisymmetric harmonic finite element representation is used to calculate shaft lateral critical speeds and perform stability analysis. Unlike a beam element model, an axisymmetric solid element representation allows the actual rotor geometry to be modeled. A Fourier series representation allows the three-dimensional shaft geometry to be modeled in two dimensions by only considering the radial and axial coordinates. Thus, the degrees of freedom of this element type are different from the usual two translations and two rotations at each node associated with bending of a three-dimensional beam element. A required gyroscopic matrix is also presented for completeness in analysis of rotating shafts. A matrix reduction technique is used to reduce the size of the shaft mass, gyroscopic, and stiffness matrices by condensing out slave degrees of freedom in terms of the retained master degrees of freedom. The formulation is applied to various examples for verification and to investigate the effect of selection of different master degrees of freedom for this element type on the results.
The Analysis of Linear Rotor-Bearing Systems: A General Transfer Matrix Method
Authors: Lee An-Chen , Shih Yuan-Pin , Kang Yuan
Published: June 2008

A general transfer matrix method (GTMM) is developed in the present work for analyzing the steady-state responses of rotor-bearing systems with an unbalancing shaft. Specifically, we derived the transfer matrix of shaft segments by considering the state variables of shaft in a continuous system sense to give the most general formulation. The shaft unbalance, axial force, and axial torque are all taken into consideration so that the completeness of transfer matrix method for steady-state analysis of linear rotor-bearing systems is reached. To demonstrate the effectiveness of this approach, a numerical example is presented to estimate the effect of three-dimensional distribution of shaft unbalance on the steady-state responses by GTMM and finite element method (FEM).
Optimal Design of Active and Semi-Active Suspensions Including Time Delays and Preview
Authors: Hac´ A. , Youn I.
Published: June 2008

Several control laws for active and semi-active suspension based on a linear half car model are derived and investigated. The strategies proposed take full advantage of the fact that the road input to the rear wheels is a delayed version of that to the front wheels, which in turn can be obtained either from the measurements of the front wheels and body motions or by direct preview of road irregularities if preview sensors are available. The suspension systems are optimized with respect to ride comfort, road holding and suspension rattle space as expressed by the mean-square-values of body acceleration (including effects of heave and pitch), tire deflections and front and rear suspension travels. The optimal control laws that minimize the given performance index and include passivity constraints in the semi-active case are derived using calculus of variation. The optimal semi-active suspension becomes piecewise linear, varying between passive and fully active system and combinations of them. The performances of active and semi-active systems with and without preview were evaluated by numerical simulation in the time and frequency domains. The results show that incorporation of time delay between the front and rear axles in controller design improves the dynamic behavior of the rear axle and control of body pitch motion, while additional preview improves front wheel dynamics and body heave.
Rotor Whirl Forces Induced by the Tip Clearance Effect in Axial Flow Compressors
Authors: Ehrich F.
Published: June 2008

It is now widely recognized that destabilizing forces, tending to generate forward rotor whirl, are generated in axial flow turbines as a result of the nonuniform torque induced by the nonuniform tip-clearance in a deflected rotor—the so called Thomas/Alford force (Thomas, 1958, and Alford, 1965). It is also recognized that there will be a similar effect in axial flow compressors, but qualitative considerations cannot definitively establish the magnitude or even the direction of the induced whirling forces—that is, if they will tend to forward or backward whirl. Applying a “parallel compressor” model to simulate the operation of a compressor rotor deflected radially in its clearance, it is possible to derive a quantitative estimate of the proportionality factor β which relates the Thomas/Alford force in axial flow compressors (i.e., the tangential force generated by a radial deflection of the rotor) to the torque level in the compressor. The analysis makes use of experimental data from the GE Aircraft Engines Low Speed Research Compressor facility comparing the performance of three different axial flow compressors, each with four stages (typical of a mid-block of an aircraft gas turbine compressor) at two different clearances (expressed as a percent of blade length)—CL/L = 1.4 percent and CL/L = 2.8 percent. It is found that the value of β is in the range of +0.27 to −0.71 in the vicinity of the stages’ nominal operating line and +0.08 to −1.25 in the vicinity of the stages’ operation at peak efficiency. The value of β reaches a level of between −1.16 and −3.36 as the compressor is operated near its stalled condition. The final result bears a very strong resemblance to the correlation obtained by improvising a normalization of the experimental data of Vance and Laudadio (1984) and a generic relationship to the analytic results of Colding-Jorgensen (1990).
A Mixture Theory for Response Fields in Complex Structures
Authors: Gillette G.
Published: June 2008

A formal procedure is developed for the calculation of fields when two (or more) component subsystems are thoroughly interlocked, so that their surface of contact extends through the total structure. Such a structure can properly be termed a structural mixture. An example is a system of frames and ribs which is completely covered by and connected to an outer skin (or shell) at a large number of points. The coupling between subsystems is accounted for in a global fashion, using Green’s functions for each of the subsystems, together with matching conditions at their interface. This leads in general to a pair of coupled integral equations, each giving the response in one of the two interpenetrating subsystems. For a disparate structural mixture comprised of “weakly-coupled” subsystems, the Green’s functions used are obtained for complementary (i.e., non-equivalent) homogeneous interface conditions. The equations can then be solved by an alternating perturbation procedure, which gives rise to a pair of coupled series. The procedure is applied to the calculation of waves in a beam stiffened at various points along its length by contact with a second subsystem. Numerical results are presented and their convergence is discussed.
Modal Analysis of a Spinning Cylindrical Shell with Interior Point or Circular Line Supports
Authors: Huang Shyh-Chin , Hsu Bih-Sheng
Published: June 2008

An approach to the modal analysis of a spinning cylindrical shell with interior multipoint or circular-line supports is developed. Receptance theory is applied for joining the shell and supports. The frequency equation and mode shapes are then formulated. Conjugate pairing in cross receptances is found in the point support case, but not in the circular line support case. Numerical results for various numbers of point supports are illustrated, and physical interpretation of those results is given. Effects of rotational speed on frequency changes are also addressed.
Theoretical and Experimental Investigation of Hydraulic Actuator Interaction in the Dynamics of a Rotating Flexible Beam
Authors: Panza M. J. , Mayne R. W.
Published: June 2008

The dynamic interaction between a rotating flexible beam and a hydraulic cylinder actuator driving the beam along its length is presented. A mathematical model is developed combining the dynamics of a continuous beam, discretized by modal analysis, to the system dynamics of the actuator. Fully coupled actuator and beam equations are generalized by introducing dimensionless parameters. The interaction between actuator and flexible beam is investigated via a reduced order model, eigenvalue analysis, and numerical simulations. Experimental results are presented to show the quality of the mathematical model and the effect of actuator parameter selection on system dynamics and beam vibration. Actuator selection concepts based on dimensionless parameters are given to provide systems with desirable dynamic performance and suppressed beam vibrations.
An Impedance Method for Dynamic Analysis of Active Material Systems
Authors: Liang C. , Sun F. P. , Rogers C. A.
Published: June 2008

This paper describes a new approach to analyzing the dynamic response of active material systems with integrated induced strain actuators, including piezoelectric, electrostrictive, and magnetostrictive actuators. This approach, referred to as the impedance method, has many advantages compared with the conventional static approach and the dynamic finite element approach, such as pin force models and consistent beam and plate models. The impedance approach is presented and described using a simple example, a PZT actuator-driven one-degree-of-freedom spring-mass-damper system, to demonstrate its ability to capture the physics of adaptive material systems, which is the impedance match between various active components and host-structures, and its utility and importance by means of an experimental example and a numerical case study. The conventional static and dynamic finite element approaches are briefly summarized. The impedance methodology is then discussed in comparison with the static approach. The basic elements of the impedance method, i.e., the structural impedance corresponding to actuator loading and the dynamic output characteristics of PZT actuators, are addressed. The advantages of using the impedance approach over conventional approaches are discussed using a simple numerical example. A comparison of the impedance method with the static and the dynamic finite element approaches are provided at the conclusion of this paper.
On Nonlinear Modes of Continuous Systems
Authors: Nayfeh A. H. , Nayfeh S. A.
Published: June 2008

We use several methods to study the nonlinear modes of one-dimensional continuous systems with cubic inertia and geometric nonlinearities. Invariant manifold and perturbation methods applied to the discretized system and the method of multiple scales applied to the partial-differential equation and boundary conditions are discussed and their equivalence is demonstrated. The method of multiple scales is then applied directly to the partial-differential equation and boundary conditions governing several nonlinear beam problems.
Response Solutions for the Vibration of a Traveling String on an Elastic Foundation
Authors: Wickert J. A.
Published: June 2008

This Tech Brief presents solutions to the response problem for the vibration of an axially-moving string that is supported by an elastic foundation. This system is of technical interest in the area of flexible media which translates at a high speed, and which is guided by air bearings or similarly modeled distributed supports. The equation of motion is dispersive and contains a skew-symmetric “Coriolis” acceleration component which derives from axial translation of the string. The equation of motion is written in the standard form for a continuous gyroscopic system, so that the string’s stability and response can be analyzed within this broader context. Available modal analysis and Green’s function methods then provide closed form expressions for the response to arbitrary initial conditions and excitation.
Relationship between Mean Value and Fourier Coefficients of a Time-Varying Function with Half-Period Rests: Theory and Application
Authors: Yu Jun-Yao
Published: June 2008

The Fourier coefficients are investigated for such a periodic time function whose magnitude keeps constant during the time of every half-period. In this case the relationship between the mean value and the Fourier coefficients is achieved using appropriate mathematical theory. It was applied successfully to the study of torsional harmonic excitations due to gas pressure in a four-cycle IC engine. A formula relating the truncated Fourier coefficient series to MIP has been established with very little error. The series simulation of Fourier coefficients is utilized in the determination and analysis of excitations.
Vibration Conveyance in Spatial-Curved Tubes
Authors: Long Y. G. , Nagaya K. , Niwa H.
Published: June 2008

The problem of inserting a long optical fiber into a long helical steel tube by means of vibration is modelled as a block repeatedly sliding and jumping inside a vibrating long tube which is in a spatial curved-line shape. Analytical models and equations are established by considering three kinds of motion states involved: relative sliding motion, flying motion, and bumping. Thorough investigations are carried out for the inclined friction with component velocities and for the oblique impact. The detailed motion of the whole response, called the “subperiodic motion,” is revealed through numerical solutions. Fundamental influences of some basic parameters on the motion of the system are discussed. Appropriate ranges for both the frequency and the amplitudes of vibration are discovered to be very narrow. Conveying materials inside vibrating tubes is quite different from, or opposite to, conveying materials on vibrating plates in ordinary use. Experimental studies confirm the theoretical analyses presented.
Vibrations of a Shallow Spherical Shell on a Kerr Foundation
Authors: Paliwal D. N. , Srivastava R.
Published: June 2008

Large amplitude free vibrations of a clamped shallow spherical shell on a Kerr-type elastic foundation model are investigated. A detailed parametric study is conducted involving geometric and elastic properties of the shell as well as representative foundation parameters. Influence of these variables on the relation between the nondimensional frequency and amplitude are discussed. Shells with immovably clamped edges are more vulnerable to the changes in the above-referred parameters than those with movable clamped edges.
Experimental Characterization of an Electrorheological Material Subjected to Oscillatory Shear Strains
Authors: Ehrgott R. C. , Masri S. F.
Published: June 2008

The coupled electrical and mechanical dynamic properties of electrorheological (ER) materials comprised of alumino-silicate in fluorinated liquids are experimentally studied to gain insight into their effectiveness for application in the area of vibration control. A prototype test device is built to subject the test materials to oscillatory shear strains over a frequency range of 1 to 50 Hz. Energy dissipation in the material is determined as a function of volume fraction, electric field, strain amplitude, and frequency. Both the pre-yield and post-yield dynamic characteristics of the material under electric field are evaluated. Results of dynamic testing showed linear visco-elastic solid behavior for the pre-yield state with the shear modulus independent of the electric field and frequency. Post-yield energy dissipation of the materials tested is found to parallel that of Coulomb damping in which the energy dissipated is independent of frequency and increases linearly with increasing strain. The method of equivalent linearization is applied to determine equivalent viscous damping and stiffness expressions in terms of the device geometry, electric field, frequency of oscillation, and amplitude of oscillation for the nonlinear post-yield behavior.
Vibration of Triangular Mindlin Plates Subject to Isotropic In-Plane Stresses
Authors: Xiang Y. , Liew K. M. , Kitipornchai S. , Wang C. M.
Published: June 2008

The influence of isotropic in-plane stresses on the fundamental vibration frequencies of thick triangular plates is investigated. Some critical buckling factors are also presented in the paper. Due to the lack of results and importance of this topic, the Rayleigh-Ritz method is applied to solve the governing eigenvalue function based on the Mindlin plate theory. The fundamental frequency parameters for triangular Mindlin plates subject to uniform tensile and compressive stresses with different combinations of free, simply supported, and clamped boundary conditions are determined. The solutions are presented in the form of design charts where the fundamental frequency parameters can easily be read for particular thickness to width ratios (t/b) and in-plane stresses. Since no other vibration solution for thick triangular plate is available, the thin triangular plate solutions obtained by setting the thickness to width ratio to be very small (say t/b = 0.001), where possible, are verified with known solutions from the open literature.
Linear Analysis Method for the Dynamic Response of a Winkler Foundation-Supported Elastic Plate Subjected to Low Velocity Projectile Impact
Authors: Huang Wei , Zou Yida
Published: June 2008

This work considers the dynamic response of an elastic plate with arbitrary boundary shape supported by a linear viscoelastic Winkler foundation, and impacted by a low velocity projectile. A nonlinear Volterra integral equation on impact force F (t) is deduced, and an effective numerical method is used to solve the equation and calculate the transverse deflection of the plate. The presence of the foundation in our problem has the effect of damping the transverse vibration of the plate owing to the absorbed energy. As a practical example, the transverse deflection of a square plate with simply supported edges impacted centrally by a sphere and the impact force are computed numerically.
Dynamic Response of Spinning Blades Subjected to Gyroscopic Motion
Authors: Young T. H. , Liou G. T.
Published: June 2008

This paper presents an investigation into the vibration and stability of a blade spinning with respect to a nonfixed axis. Due to the motion of the spin axis, parametric instability of the blade may occur in certain situations. In this work, the discretized equations of motion are first formulated by the finite element technique. Then the system equations are transformed, by a special modal analysis procedure, into independent sets of first-order simultaneous differential equations. Each set of differential equations is solved analytically by the method of multiple scales if the precessional speed of the spin axis is assumed to be small compared to the spin rate of the blade, yielding the system response and the expressions for the boundaries of the unstable regions. Finally, the effects of system parameters on the changes in these boundaries are studied numerically.
Rotational Response and Slip Prediction of Serpentine Belt Drive Systems
Authors: Hwang S.-J. , Perkins N. C. , Ulsoy A. G. , Meckstroth R. J.
Published: June 2008

A nonlinear model is developed which describes the rotational response of automotive serpentine belt drive systems. Serpentine drives utilize a single (long) belt to drive all engine accessories from the crankshaft. An equilibrium analysis leads to a closed-form procedure for determining steady-state tensions in each belt span. The equations of motion are linearized about the equilibrium state and rotational mode vibration characteristics are determined from the eigenvalue problem governing free response. Numerical solutions of the nonlinear equations of motion indicate that, under certain engine operating conditions, the dynamic tension fluctuations may be sufficient to cause the belt to slip on particular accessory pulleys. Experimental measurements of dynamic response are in good agreement with theoretical results and confirm theoretical predictions of system vibration, tension fluctuations, and slip.
Nonlinear Dynamics of an Oilless Linear Drive Reciprocating Compressor
Authors: Minas C.
Published: June 2008

Two modeling methodologies of the dynamics of a motor-compressor system are presented. The first approach considered only the mechanical system subjected to a sinusoidal input force with the pressure term in the equation of motion treated as a nonlinear stiffness term. The second methodology consisted of a mathematical model that couples the electromagnetic and thermodynamic equations to the dynamic equations that describe the motion of the piston. The mathematical model which consisted of a set of four first order simultaneous nonlinear time varying differential equations was solved by numerical integration routines that use the Adams-Moulton method with an adaptive integration step. The two methodologies are illustrated through an example. Steady-state operation was shown to be reached rapidly after a 0.13s transient. An analysis at various amplitudes and frequencies of the input voltage in the driver-coil of the motor showed the amplitude dependence of the natural frequency of the mechanical system, and a heavily damped system when operating at the design amplitude. The most efficient frequency of operation was also determined for a variety of required mass flow rates.
Experimental Modal Analysis of a Suspension Assembly Loaded on a Rotating Disk
Authors: Wilson C. J. , Bogy D. B.
Published: June 2008

An experimental modal analysis system, which has been shown to be effective in the study of small structures, is utilized to analyze the interaction of the disk and the suspension assembly in a computer disk drive. A thorough understanding of the interaction of these structures is obtained by determining the modal parameters for each of the components in an uncoupled state and in a coupled state with the disk both stationary and rotating. It is shown that when a natural frequency of the suspension is close to that of the disk, two system resonant frequencies are created when the components are coupled together.
Full Beam Formulation of a Rotating Beam-Mass System
Authors: Fallahi B. , Lai S. H.-Y. , Gupta R.
Published: June 2008

In this study a comprehensive approach for modeling flexibility for a beam with tip mass is presented. The method utilizes a Timoshenko beam with geometric stiffening. The element matrices are reported as the integral of the product of shape functions. This enhances their utility due to their generic form. They are utilized in a symbolic-based algorithm for the automatic generation of the element matrices. The time-dependent terms are factored after assembly for better computational implementation. The effect of speed and tip mass on cross coupling between the elastic and rigid body motions represented by Coriolis, normal and tangential accelerations is investigated. The nonlinear term (geometric stiffening) is modeled by introducing a tensor which plays the same role as element matrices for the linear terms. This led to formulation of the exact tangent matrix needed to solve the nonlinear differential equation.
Vibration of Clamped Circular Symmetric Laminates
Authors: Liew K. M.
Published: June 2008

Treated in this paper is the free-flexural vibration analysis of symmetrically laminated thin circular plates. The total energy functional for the laminated plates is formulated where the pb-2 Ritz method is applied for the solution. The assumed displacement is defined as the product of (1) a two-dimensional complete polynomial function and (2) a basic boundary function. The simplicity and accuracy of the numerical procedure will be demonstrated by solving some plate examples. In the present study, the effects of material properties, number of layers and fiber stacking sequences upon the vibration frequency parameters are investigated. Selected mode shapes by means of contour plots for several 16-ply laminated plates with different fiber stacking sequences and composite materials are presented. This study may provide valuable information for researchers and engineers in design applications. In addition, the present solution plays an important role in increasing the existing data base for future references.
Vibration of an Eccentrically Clamped Annular Plate
Authors: Tseng J.-G. , Wickert J. A.
Published: June 2008

Small amplitude vibration of an eccentric annular plate, which is free along its outer edge and clamped along the interior, is investigated through experimental and analytical methods. A disk with this geometry, or a stacked array in which the clamping and symmetry axes of each disk are nominally coincident, is common in data storage and brake systems applications. In the present case, the geometric imperfections on the boundary can have important implications for the disk’s dynamic response. Changes that occur in the natural frequency spectrum, the mode shapes, and the free response under eccentric mounting are studied through laboratory measurements and an approximate discrete model of the plate. The natural frequencies and modes are found through global discretization of the Kamke quotient for a classical thin plate. For the axisymmetric geometry, the natural frequencies of the “sine” and “cosine” vibration modes for a specified number of nodal diameters are repeated. With increasing eccentricity, on the other hand, each pair of repeated frequencies splits at a rate that depends on the number of nodal diameters. Over a range of clamping and eccentricity ratios, the model’s predictions are compared to the measured results.
Higher Harmonic Oscillations in a Noncontacting FMR Mechanical Face Seal Test Rig
Authors: Lee An Sung , Green Itzhak
Published: June 2008

In order to investigate experimentally the dynamic behavior of a noncontacting flexibly mounted rotor (FMR) mechanical face seal a test rig was designed and built. Test results showed that the FMR seal was vulnerable to higher harmonic oscillations with frequencies that are integer multiples of the shaft speed. Because system nonlinearities can cause higher harmonic oscillations, the dynamic moments acting on the rotor are derived to include the effects of imbalance and axial offset of the rotor. The analysis reveals that the nonlinear terms involved are of second order and generally can be neglected. Investigation is then directed to analyze the possibility of rubbing contact between the rotor and the stator. Rubbing contact can occur as a result of a high relative angular misalignment between the rotor and the stator. A contact kinematics model is proposed and a Fourier series analysis is performed on the resulting rotor response. The analysis shows that the proposed response contains higher harmonics. Fourier series expansion and numerical filtering of a sampled rotor response from the test rig yield resembling signals which contain higher harmonics. This suggests that rubbing contact is the source of higher harmonic oscillations. Design modification to the rotor flexible support system resulted in a virtual elimination of higher harmonic oscillations.
Stability of Nonconservatively Elastic Systems Using Eigenvalue Sensitivity
Authors: Chen Lien-Wen , Ku Der-Ming
Published: June 2008

The stability of a cantilever column, carrying a concentrated mass at the free end and resting on an elastic foundation of the Winkler-type, subjected to uniformly distributed in-plane follower forces is studied by “Timoshenko beam theory” finite elements. In order to more quickly and efficiently obtain the critical load for such a nonconservative system, a simple and cost-effective numerical technique which utilizes the eigenvalue sensitivity with respect to the follower force is introduced instead of the conventional trial-and-error technique. The high accuracy and rapid rate of convergence through the combination of the present finite element model and the solution technique are demonstrated with the numerical example given. The influence of some system parameters on the critical load is also discussed.
Window Functions for the Calculation of the Time Domain Averages of the Vibration of the Individual Planet Gears and Sun Gear in an Epicyclic Gearbox
Authors: McFadden P. D.
Published: June 2008

An existing technique which enables the estimation of the time domain averages of the tooth meshing vibration of the individual planet and sun gears in an epicyclic gearbox from measured vibration signals has been revised. A key feature of the existing technique is the sampling of the vibration signal within a rectangular window in the time domain when one of the planet gears is close to the vibration transducer. The revised technique permits the use of other window functions, and a detailed analysis shows that the errors in the estimate of the time domain average can be expressed in terms of the window function. Several suitable window functions which enable a reduction in the level of the errors are demonstrated by numerical examples and by the analysis of data from a test on a helicopter gearbox with deliberate damage to one of the planet gears.
Bending and Shear Damping in Beams: Frequency Domain Estimation Techniques
Authors: Banks H. T. , Wang Y. , Inman D. J.
Published: June 2008

In this paper we consider damping mechanisms in the context of dynamic beam models. We summarize previous efforts on various damping models (strain rate or Kelvin-Voigt, time hysteresis (Boltzmann), spatial hysteresis, bending rate/square root) for the Euler-Bernoulli beam theory. The Euler-Bernoulli theory is known to be inadequate for experiments in which high frequency modes have been excited. In such cases the Timoshenko theory may be more appropriate; we consider a number of damping hypotheses for this theory. Corresponding models are proposed and compared to experimental data in the context of parameter estimation or identification problems formulated in the frequency domain. Theoretical results related to the convergence of approximations to these infinite dimensional distributed parameter system estimation problems are presented. Associated computational findings for specific beam experiments are discussed.
Energy Transfer From High-to Low-Frequency Modes in a Flexible Structure via Modulation
Authors: Nayfeh S. A. , Nayfeh A. H.
Published: June 2008

An experimental study of the response of axially-symmetric (i.e., circular cross-section) cantilever beams to planar external excitations is presented. Because of the axial symmetry, one-to-one internal resonances occur at each natural frequency. These resonances cause the planar motions to lose stability and nonplanar (whirling) motions are observed. Under certain conditions, periodically-and chaotically-modulated motions may occur. In addition, when the beam is excited near one of its high natural frequencies, large first-mode responses accompanied by slow modulations of the amplitudes and phases of high-frequency modes are observed. This interaction between high-and low-frequency modes may be extremely dangerous because the amplitudes of the responses of the low-frequency modes can be very large compared with those of the directly excited high-frequency modes.
An Improved Theoretical Model of Acoustic Agglomeration
Authors: Song L. , Koopmann G. H. , Hoffmann T. L.
Published: June 2008

An improved theoretical model is developed to describe the acoustic agglomeration of particles entrained in a gas medium. The improvements to the present theories are twofold: first, wave scattering is included in the orthokinetic interaction of particles and second, hydrodynamic interaction, shown to be an important agglomeration mechanism for certain operation conditions, is incorporated into the model. The influence of orthokinetic and hydrodynamic interactions introduce associated convergent velocities that cause particles to approach each other and collide. The convergent velocities are related with an acoustic agglomeration frequency function (AAFF) through a semi-statistical method. This function is the key parameter for the theoretical simulation of acoustic agglomeration.
A Substructural Control Technique for High-Order Systems
Authors: Ahmadian M.
Published: June 2008

A substructural control technique consisting of local and global controllers is proposed for high-order systems. The global controllers are used to minimize the effect of coupling between substructures, whereas the local controllers are employed to accomplish optimal performance and stability. A set of stability conditions based on the properties of the substructures is presented for the global stability of the structure. The advantages of the proposed technique are demonstrated using a structure consisting of two flexible panels and a rigid hub. The examples show that the proposed substructural control technique is more computationally efficient than a centralized control approach, and it can effectively control the structure and maintain stability, with a slight increase in the control inputs.