bluuebunny/crossref_metadata_2025 huggingface dataset:
Vibration Suppression Using a Proofmass Actuator Operating in Stroke/Force Saturation
Authors: Lindner D. K. , Celano T. P. , Ide E. N.
Published: June 2008

We consider proofmass actuators for vibration suppression in flexible structures. Proofmass actuators appear to have a significant force-to-weight ratio over other types of actuators; hence, there has been considerable interest in them recently. These actuators, however, have a maximum force capability imposed in part by the stroke length of the proofmass. This nonlinearity is difficult to handle because this constraint cannot be violated (unlike saturation of electronic devices). Furthermore, this constraint is peculiar to this type of actuator. In this paper we consider the control loop structure of a feedback control system which contains a proofmass actuator for vibration suppression. This loop structure is decomposed into inner control loops directly related to the actuator and outer loops which add damping to the structure. The inner loops determine the frequency response of the actuator. Evidently, when the frequency response of the actuator is matched to the stroke/force saturation curve, the actuator is most effective in the vibration suppression loops. Since the stroke/force saturation curve is characterized by the stroke length, mass of the proofmass, and the maximum current delivered by motor electronics, this actuator can be easily sized for a particular application. We also discuss the interaction between the inner loops around the actuator and the structure (with the vibration loops open). To illustrate our results, we consider linear DC motors as proofmass actuators for the COFS-I Mast. To discuss the interaction the actuator and the structure, we develop a simple result based on classical control theory. This result is of independent interest since it leads to a simple procedure for designing low order compensators for single-input-single-output systems with poles near the imaginary axis.
Nonlinear Dynamic Modelling of a Revolute-Prismatic Flexible Composite-Material Robot Arm
Authors: Gordaninejad F. , Azhdari A. , Chalhoub N. G.
Published: June 2008

In this work, a nonlinear dynamic model is derived to study the motion of a planar robot arm consisting of one revolute and one prismatic joint. Both links of the arm are considered to be flexible and are assumed to be constructed from either isotropic conventional metallic materials or anisotropic laminated fibrous composite materials. The model is derived based on the Timoshenko beam theory in order to account for the rotary inertia and shear deformation. In addition, a nonlinear strain-displacement field is implemented to consider the large deformation of the arm. The deflections of the links are discretized by using a shear-deformable beam finite element. The governing equations of motion are derived from Hamilton’s principle. The digital simulation studies examine the combined effects of geometric nonlinearity, rotary inertia, and shear deformation on the arm’s end effector displacements. Furthermore, effects of the fiber’s angle and material orthotropy on the end effector displacements and maximum normal bending stress are studied.
The Origin of Permanent Magnet Induced Vibration in Electric Machines
Authors: Rahman B. S. , Lieu D. K.
Published: June 2008

A principal source of vibration in permanent magnet motors and generators is the induced travelling forces from the rotating permanent magnets acting on the stator. The form of the magnetic field and resulting forcing function in the airgap of such machines is critical. The stator is modelled as a solid ring, with no teeth. Various motor parameters were investigated, including the effects of radial versus parallel magnetization, magnetization tolerances, and radial offset. The results were determined with analytical and FEM models. It was concluded that radial magnetization of the permanent magnets was preferable for both vibration and motor performance. Magnetization tolerances and radial offsets yielded a relatively more populated frequency spectrum for the forcing function and thus could lead to a greater probability of resonant modes being excited in the surrounding structure.
Influence of Impeller Shroud Forces on Turbopump Rotor Dynamics
Authors: Williams J. P. , Childs D. W.
Published: June 2008

The shrouded-impeller leakage path forces calculated by Childs (1987) have been analyzed to answer two questions. First, because of certain characteristics of the results of Childs, the forces could not be modeled with traditional approaches. Therefore, an approach has been devised to include the forces in conventional rotordynamic analyses. The forces were approximated by traditional stiffness, damping and inertia coefficients with the addition of whirl-frequency-dependent direct and cross-coupled stiffness terms. The forces were found to be well-modeled with this approach. Finally, the effect these forces had on a simple rotor-bearing system was analyzed, and, therefore, they, in addition to seal forces, were applied to a Jeffcott rotor. The traditional methods of dynamic system analysis were modified to incorporate the impeller forces and yielded results for the eigenproblem, frequency response, critical speed, transient response, and an iterative technique for finding the frequency of free vibration as well as system stability. All results lead to the conclusion that the forces have little influence on natural frequency but can have appreciable effects on system stability. Specifically, at higher values of fluid swirl at the leakage path entrance, relative stability is reduced. The only unexpected response characteristics that occurred are attributed to the nonlinearity of the model.
A Practical Technique for Spectral Analysis of Nonlinear Systems Under Stochastic Parametric and External Excitations
Authors: Chang R. J.
Published: June 2008

A practical approach is developed for analyzing the spectral response of a nonlinear system subjected to both parametric and external Gaussian white noise excitations. The technique is implemented through the combined methods of equivalent external excitation and equivalent linearization to derive an equivalent linear system under equivalent external noise excitation. The spectral response is then obtained through utilizing the input/output spectral relation and covariance matching condition. A parametric noise excited linear system, Duffing oscillator, and nonlinear system with hysteretic nonlinearity are selected for investigation. The validity of the proposed method for analyzing spectral response is further supported by some analytical solutions and FFT technique through Monte Carlo simulations.
Acoustic Emission Waves in Perfect-Bonded Bimaterial Plates: Numerical Simulations and Experiments
Authors: Wu Tsung-Tsong , Kuo Chiu-Long
Published: June 2008

This paper utilized finite difference schemes to simulate the propagation of acoustic emission (AE) waves in isotropic, anisotropic plates as well as perfect-bonded bimaterial composite plates. Acoustic emission experiments were conducted to study the propagation of elastic waves in the aforementioned plates. The numerical simulated wave responses were in accordance with those measured experimentally. In the case of AE waves in perfect-bonded bimaterial composite plates, the agreements between the numerical and experimental results imply a possible application to the detection of perfect bonding. Demonstration of the effect of curing time on the acoustic emission waves in a bimaterial plate is also presented.
Approximate Analysis of the Forced Vibration Response of Plates
Authors: Leissa A. W. , Chern Yi-Tzong
Published: June 2008

An approximate method is presented for the forced vibration analysis of plates. It is applicable in excitation frequency ranges close to resonances. A displacement shape for the plate in the resonance region is assumed, which is either an exact or approximate representation for the corresponding free vibration mode shape. The response amplitude is determined from a proper energy balance. The method is demonstrated for two types of plates—simply supported rectangular and clamped circular—subjected to uniform transverse exciting pressure. Special considerations are indicated for cases when degenerate or closely spaced resonant frequencies are present. Both viscous and material damping are treated. Numerical comparisons between approximate and exact forced vibration solutions are made to demonstrate the accuracy of the method.
A Simple Technique for the Rapid Estimation of the Optimal Support Locations for a Vibrating Plate
Authors: Pitarresi J. M. , Kunz R. J.
Published: June 2008

This paper is aimed at presenting a simple technique for the rapid estimation of the optimal point support locations of vibrating plates. Using a two-dimensional nonlinear least-squares fit of natural frequency versus support location data, along with the concept of response surfaces, a difficult design optimization problem involving changing boundary conditions is transformed to a much simpler, approximate form. By using classical optimization theory, the estimated optimal location of the support can then be readily found. The computations for the formation of the response function and its optimum can be readily carried out on a personal computer using a spreadsheet program. The validity of this approach is demonstrated through a number of examples using analytical, computational, and experimental data. The technique is well suited to preliminary design investigations where a rapid but accurate estimation of the support location is required. Finally, a key advantage of the proposed method is that it can be used with data from any analytical, computational, or experimental effort, including any combination of the above.
On the Stability of Chain Drive Systems Under Periodic Sprocket Oscillations
Authors: Wang K. W.
Published: June 2008

Experimental observations have shown that periodic torsional oscillations of engine camshafts induced by powertrain loads can cause significant tension variation in the timing chain and magnify the chain transverse vibrations and noise level. This result indicates that the sprocket dynamic characteristics and the chain vibration behavior are closely coupled. The chain drive models to-date are not able to address these phenomena. This paper presents a nonlinear model of an integrated chain drive system which couples the sprocket motion with the transverse and longitudinal vibration of the axially moving chain spans. With this model, the effects of the sprocket shaft periodic loads upon the total system are investigated. It is concluded that the sprocket oscillations will cause chain longitudinal vibrations. This could destabilize the system and induce the chains to undergo large transverse vibration. Both the subharmonic and summation types of parametric resonance are found and the instability regions are derived. The effects of various system parameters, such as the sprocket inertia, the chain speed, and the speed dependent excitation frequencies upon the instability regions have been studied. The significance of the gyroscopic terms of the stability boundary has been shown.
Vibration Damping Through Liquid Sloshing, Part 2: Experimental Results
Authors: Welt F. , Modi V. J.
Published: June 2008

Experiments designed to evaluate performance of partially filled torus shaped nutation dampers, undergoing steady-state forced excitation in translational motion, are described. The forces exerted by the fluid on the damper walls are measured over a range of system parameters. Results suggest that low liquid heights and large diameter ratios with the system operating at liquid sloching resonance lead to increased damping. On the other hand, low Reynolds numbers and presence of obstacles, such as baffles, tend to reduce the peak efficiency by restricting the action of the free surface. The theory, based on the potential flow approach and corrected for viscosity near the solid boundary, generally yields the right trends while underestimating the amount of dissipation within the torus. A flow visualization study qualitatively confirms the nature of the mode shapes predicted by the theory.
Finite Element Modeling of Dynamic Behavior of Some Basic Structural Members
Authors: Engels R. C.
Published: June 2008

A method is described to model the dynamics of finite elements. The assumed modes method is used to show how static shape functions approximate the element mass distribution. The deterioration of the modal content of a model can be linked to the neglect of interface restrained assumed modes. Restoration of a few of these modes leads to higher accuracy with fewer generalized coordinates compared to the standard consistent mass matrix approach. Also, no need exists for subdivision of basic elements such as rods and beams. The mass and stiffness matrices for several basic elements are derived and used in demonstration problems.
Advanced Analysis of Multi-Ring Liquid Seals
Authors: Reedy S. W. , Kirk R. G.
Published: June 2008

The equilibrium position of multi-ring seal assemblies is of major importance to the designer of high pressure centrifugal compressors. Typical computer codes now use a curve-fit of the Short Bearing Sommerfeld Number for eccentricity evaluation with the assumption that all rings in the assembly will always operate at the same eccentricity. The results from the recently developed seal analysis program, SEALS, have shown that the equal eccentricity assumption for multi-ring seals is questionable. This paper will review the analysis procedure used in SEALS, and present the results of an eccentricity evaluation comparison with a seal analysis program currently being used in industry.
Damped Absorber Optimization and Stability for Semi-Definite Systems Exhibiting Unstable Self-Excitation During Start-Up
Authors: Shadley J. R. , Sorem J. R.
Published: June 2008

Stability is examined with respect to the torque in the elastic element between motor and load in semi-definite systems exhibiting unstable self-excitation during start-up. Equations are provided for optimizing a motor-mounted damped absorber to minimize the torque fluctuations in the shafting between motor and load in semi-definite systems. Minimum damper inertia needed to stabilize the system is computed assuming optimum damping. Stability and damper optimization equations are applied to two cases involving unstable self-excitation in electric submersible pump systems. In the first case, unstable growth of torque amplitude in shafting between an electric induction motor and an inertial load was observed during start-up in laboratory testing. A computer simulation of the system dynamics demonstrated that the torque could be stabilized by adding a damped absorber to the motor. In a computer simulation for the second case, unstable torque fluctuations in the shafting of an electric submersible pump system were dramatically reduced by the addition of a damped absorber; however, stability was not achieved until the damper inertia was sufficiently increased. Stability is not always required for safe operation of electric submersible pumps. A computational model of the system dynamics during startup should be used to determine when stability is required.
Rotor Transient Response Induced by Losses in the Rotating Mass
Authors: Kujath Marek R. , Wanping Zheng
Published: June 2008

The topic of the paper has been focused on the physical behavior of rotors subjected to losses in the rotating mass and on developing methods for detection of the presence and the extent of changes in the rotor. The developed diagnostic techniques have been designed to utilize the vibration data collected during a normal operation and at a single running speed alone. One of the main concepts employed in the described procedures consists in isolation, observation, and processing of transient vibrations which follow a separation of mass. Several methods of extracting the transients from experimental data have been investigated and their advantages and limitations have been discussed. In order to study the mass loss phenomenon a special rotor-bearing system has been developed. The design allows frequent repetition of the mass release experiment. The paper contains detailed description of the mass release mechanism. An example of application of the experimental data for detection of the extent of changes in the rotor has been included.
Free and Forced Longitudinal Vibrations of a Cantilevered Bar With a Crack
Authors: Collins K. R. , Plaut R. H. , Wauer J.
Published: June 2008

Longitudinal vibrations of a cantilevered bar with a transverse crack are investigated. For undamped, unforced vibrations, frequency spectra are computed and the effects of the crack location and compliance on the fundamental natural frequency are determined. For vibrations caused by a distributed, longitudinal, harmonic force, the steady-state amplitude of motion of the free end is plotted as a function of the forcing frequency, crack location, and crack compliance, and frequency spectra are also obtained. Results for a breathing crack are compared to those for a crack which remains open and those for an uncracked bar.
Acoustic Design Sensitivity for Structural Radiators
Authors: Cunefare K. A. , Koopmann G. H.
Published: June 2008

An analysis technique designated as acoustic design sensitivity (ADS) analysis is developed via the numerical treatment of a discrete quadratic expression for the total acoustic power radiated by a three-dimensional extended structure. A boundary element formulation of the Helmholtz Integral Equation is the basis of the analysis leading to the quadratic power expression. Partial differentiation of the quadratic power expression with respect to a known surface velocity distribution leads to a sensitivity distribution, represented by a distribution of values on the surface of a structure. The sensitivity values represent a linear approximation to the change in the total radiated power caused by changes in the surface velocity distribution. For a structure vibrating with some portions of its surface rigid and such that the acoustic wavelength is long compared to a characteristic dimension of the structure, ADS analysis reveals that the rigid surfaces strongly influence the sensitivity distribution, as expected. Under such conditions, the rigid surfaces can exhibit the maximum value of the entire sensitivity distribution, even though the acoustic intensity is identically zero on a rigid surface. As the frequency increases, and the acoustic wavelength becomes comparable to a characteristic dimension of the structure, the position of the maximum value of the sensitivity distribution will coincide with the region of the maximum surface acoustic intensity.
A Transfer Matrix Technique for Evaluating the Natural Frequencies and Critical Speeds of a Rotor With Multiple Flexible Disks
Authors: Wu F. , Flowers G. T.
Published: June 2008

The influence of disk flexibility on the rotordynamical behavior of turbomachinery is a topic that is of some concern to designers and analysts of such equipment. Research in this area has indicated that disk flexibility may significantly alter the dynamical behavior of a rotor system. This research effort is concerned with developing a procedure to account for disk flexibility which can readily be used for investigating how such effects might influence the natural frequencies and critical speeds of practical rotor systems. A transfer matrix procedure is developed in this work in which the disk flexibility effects are accounted for by means of additional terms included in the transfer matrix formulation. In this way the efficiency and practicality of the transfer matrix method is retained. To demonstrate this technique, a simple rotor system is studied for the effect of disk flexibility and the results discussed.
Methods for Speeding Up the Boundary Element Solution of Acoustic Radiation Problems
Authors: Kirkup S. M. , Henwood D. J.
Published: June 2008

Methods for speeding up the boundary element solution of acoustic radiation problems are considered. The methods are based on solving the integral equation formulation of Burton and Miller for the exterior Helmholtz equation over a range of frequencies simultaneously. Methods for speeding up the computation of the discrete forms of the integral operators and the solution of the linear systems that arise in the boundary element method are considered. A particular implementation of speedup methods is described. Results from the application of this to test problems are given.
Fatigue Life Prediction Using Frequency Response Functions
Authors: Sanliturk K. Y. , Imregun M.
Published: June 2008

This paper presents a method for fatigue life prediction of engineering components subjected to dynamic loads. It is based on the determination of the nominal stress at the crack position using frequency response functions and this in turn enables the prediction of dynamic fatigue life under forced vibration. The main advantage of this approach lies in the fact that stresses used for fatigue life prediction are determined via a vibration analysis and hence not only elastic but also inertia and damping forces are included in the model. The implementation of the technique is discussed in the case of a bladed-disc assembly where single-blade mistuning is caused by a fatigue crack. It is believed that the proposed method has promising implications for safer designs and also for the prediction of inspection intervals, especially in rotating machinery applications where such considerations are of paramount importance.
Wet Modes of Submerged Structures—Part 2: Applications
Authors: Daddazio R. P. , Ettouney M. M. , Abboud N.
Published: June 2008

Using the wet mode methodology described in Part I of this paper, we examine the harmonic response of an elastic shell in an infinite acoustic medium subjected to an incident pressure wave. Both surface and far field responses are studied utilizing this computational procedure. We investigate the sensitivity of response with respect to changes in frequency of oscillation of the system and geometry of the submerged structure. In addition, we compare the wet modes of the system and in vacuo modes of the structure. The propagation of the surface velocity wet modes to the far field is illustrated. The contribution of the individual modes to the far field pressure and surface velocities as a function of frequency and location is presented.
Dynamic Scaling of Flexible Structures With Viscoelastic Components
Authors: Alberts Thomas E. , Xia Houchun , Chen Yung
Published: June 2008

Laboratory dynamic testing of large and complex space structures can be difficult and expensive, if practical at all. The use of dynamically scaled test articles is a standard approach to laboratory testing which helps to avoid these problems. The theory and practice of dynamic scaling for elastic structures are well established and validated; however, the issue of scaling structures with viscoelastic components has not been thoroughly investigated. In a structure that is “replica scaled” by a factor 1/λ, the natural frequencies are each scaled by a factor λ. For proper dynamic scaling, each corresponding damping ratio should be unchanged from that of the original full scale structure. The difficulty that arises with structures incorporating viscoelastic components is that the viscoelastic material properties vary with frequency in a nonlinear fashion. Thus, for a particular mode of a scaled model, the viscoelastic material’s damping properties are evaluated at a frequency which is modified by a factor 1/λ and as a consequence the damping ratio does not scale properly. To solve this problem, the authors propose taking advantage of the temperature dependence of viscoelastic material properties. By appropriately controlling the experimental temperature of the scaled structure, it is possible to obtain accurate dynamic scaling results. In this paper, the proposed frequency-temperature compensation method of dynamic scaling for viscoelastically damped structures is developed and experimentally validated.
Transient Dynamic Analysis of Rotors Using SMAC Techniques: Part 1, Formulation
Authors: Ratan S. , Rodriguez J.
Published: June 2008

A new method is introduced for performing transient dynamic analysis of rotor systems using a Successive Merging and Condensation (SMAC) technique. This approach can be applied to rotor analysis problems formulated with the finite element method. Condensation is done on the partitioned equations of motions for an element, and the result is merged into the next element’s equations of motion. Such manipulations result in a reduced size for the system’s matrices, producing a computationally more efficient scheme. After the boundary conditions are applied, a time-marching scheme provides the transient solution at each time step.
Transient Dynamic Analysis of Rotors Using SMAC Techniques: Part 2, Numerical Study
Authors: Ratan S. , Rodriguez J.
Published: June 2008

A new method for performing transient time-domain analysis of rotor systems using a Successive Merging and Condensation (SMAC) technique was introduced in Part 1. This approach can be applied to rotor analysis problems formulated with the finite element method. A numerical study, including examples, comparison of methods, and performance evaluation, is presented here. Validation and applicability of the SMAC method are illustrated with three examples: conservative, nonconservative, and nonlinear. The SMAC algorithm is then compared to the following methods: Transfer Matrix Method (TMM), Modal Superposition Method, and Runge-Kutta Method, and is demonstrated to be computationally more efficient in terms of CPU time and storage space. The issues of stability and time-step size are also studied.
Experimental Verification of the Asymptotic Modal Analysis Method as Applied to a Rectangular Acoustic Cavity Excited by Structural Vibration
Authors: Peretti L. F. , Dowell E. H.
Published: June 2008

An experiment was performed on a rigid wall rectangular acoustic cavity driven by a flexible plate mounted in a quarter of one end wall and excited by white noise. The experiment was designed so that the assumptions of Asymptotic Modal Analysis (AMA) were satisfied for certain bandwidths and center frequencies. Measurements of sound pressure levels at points along the boundaries and incrementally into the interior were taken. These were compared with the theoretical results predicted with AMA, and found to be in good agreement, particularly for moderate (1/3 octave) bandwidths and sufficiently high center frequencies. Sound pressure level measurements were also taken well into the cavity interior at various points along the 5 totally rigid walls. The AMA theory, including boundary intensification effects, was shown to be accurate provided the assumption of large number of acoustic modes is satisfied, and variables such as power spectra of the wall acceleration, frequency, and damping are slowly varying in the frequency bandwidth.
The Accuracy of Doubly Asymptotic Approximations for an Acoustic Half-Space
Authors: Hasheminejad M. , Geers T. L.
Published: June 2008

The accuracy of doubly asymptotic approximations (DAAs) for acoustic half-space problems is assessed by examining their performance for a canonical problem in bispherical coordinates. Exact specific acoustic impedance curves for axisymmetric modal vibrations of a spherical surface near a planar boundary are generated, and corresponding curves based on the first-order DAA and the curvature-corrected DAA are compared with their exact counterparts. The comparisons show that the curvature-corrected DAA is substantially more accurate than the first-order DAA. Also, the curvature-corrected DAA is found to be satisfactory for broad-band excitations regardless of the sphere’s proximity to a compliant (zero-pressure) surface; for a rigid surface, the approximation is satisfactory only if the sphere is located at least one diameter away from the boundary.
A Spectral Element Approach to Wave Motion in Layered Solids
Authors: Rizzi S. A. , Doyle J. F.
Published: June 2008

A matrix methodology similar to that of the finite element method is developed for the analysis of stress waves in layered solids. Because the mass distribution is modeled exactly, the approach gives the exact frequency response of each layer. The fast Fourier transform and Fourier series are used for inversion to the time/space domain. The impact of a structured medium with multiple layers is used to demonstrate the method. Comparison with existing propagator and direct global matrix methods show the present approach to be computationally more efficient.
Modeling of Linear Viscoelastic Space Structures
Authors: McTavish D. J. , Hughes P. C.
Published: June 2008

The GHM Method provides viscoelastic finite elements derived from the commonly used elastic finite elements. Moreover, these GHM elements are used directly and conveniently in second-order structural models jut like their elastic counterparts. The forms of the GHM element matrices preserve the definiteness properties usually associated with finite element matrices—namely, the mass matrix is positive definite, the stiffness matrix is nonnegative definite, and the damping matrix is positive semi-definite. In the Laplace domain, material properties are modeled phenomenologically as a sum of second-order rational functions dubbed mini-oscillator terms. Developed originally as a tool for the analysis of damping in large flexible space structures, the GHM method is applicable to any structure which incorporates viscoelastic materials.
Nonlinear Effects of a Modal Domain Optical Fiber Sensor in a Vibration Suppression Control Loop for a Flexible Structure
Authors: Lindner D. K. , Zvonar G. A. , Baumann W. T. , Delos P. L.
Published: June 2008

Recently, a modal domain optical fiber sensor has been demonstrated as a sensor in a control system for vibration suppression of a flexible cantilevered beam. This sensor responds to strain through a mechanical attachment to the structure. Because this sensor is of the interferometric type, the output of the sensor has a sinusoidal nonlinearity. For small levels of strain, the sensor can be operated in its linear region. For large levels of strain, the detection electronics can be configured to count fringes. In both of these configurations, the sensor nonlinearity imposes some restrictions on the performance of the control system. In this paper we investigate the effects of these sensor nonlinearities on the control system, and identify the region of linear operation in terms of the optical fiber sensor parameters.
The Vibration Damping Effect of an Electrorheological Fluid
Authors: Austin S. A.
Published: June 2008

The attenuation of longitudinal vibrations in structures can be achieved through a change in the impedance of the structure. This impedance change can be produced by an electrorheological fluid. The transmission of a known vibration input along a test structure will be correlated to the impedance characteristics of the electrorheological fluid. This impedance characteristic of the fluid will be expressed in terms of the applied electric field. The attenuation characteristics of the electrorheological fluid on longitudinal vibration have been presented through experimental and numerical results. The results of this study showed an attenuation of 4 dB in the transmissibility of acceleration from the forward to the aft ends of the test structure. This level can be increased by using a fluid possessing a lower zero state viscosity. A secondary result of this investigation is understanding the physics of the damping mechanism in the test module when the electric field was increased from 1.2 kV/mm to the value of 1.6 kV/mm. During this increase in the electric field, the logarithmic decrement increased by more than a factor of three. The transmissibility data also shows that the resonant frequency decreased.
Effect of Axial Vibrations on the Dynamics of a Helical Gear Pair
Authors: Kahraman A.
Published: June 2008

In this paper, a linear dynamic model of a helical gear pair has been developed. The model accounts for the shaft and bearing flexibilities, and the dynamic coupling among the transverse, torsional, axial and rotational (rocking) motions due to the gear mesh. The natural frequencies and the mode shapes have been predicted, and the modes which are excited by the static transmission error have been identified. The forced response due to the static transmission error has also been predicted, including the dynamic mesh and bearing forces. A parametric study has been performed to investigate the effect of the helix angle on the free and forced vibrational characteristics of the gear pair. It has been shown that the helix angle can be neglected in predicting the natural frequencies and the dynamic mesh forces. An accurate prediction of dynamic bearing forces and moments requires inclusion of the helix angle in the analysis.
Stability and Nonlinear Dynamics of a Horizontally Base-Excited Rigid Rod With Unsymmetric End Stiffnesses
Authors: Cheng J. K. , Wang K. W.
Published: June 2008

This paper presents a dynamic analysis of a horizontally base-excited rigid rod with unsymmetric end stiffnesses. This is to model a shaker/mould structure with gripper imperfections. The study explains the large rotational and transverse vibrations of the mould at specific operating frequencies observed in the experiments. The governing equations consist of a time-dependent coefficient which indicates the existence of parametric excitation effects. It is concluded that differences between the gripper stiffnesses are responsible for this phenomenon and could destabilize the system. The value of the time-varying parameter is related to the horizontal vibration amplitude of the mould and hence is a function of the system parameters and excitation frequency. The mould’s rotational motion is directly parametrically excited while its transverse vibration is excited indirectly through coupling with the rotational motion. A thorough analysis of this class of mechanical systems has not been performed in the past. In this research, studies are conducted to identify the contributions of various system parameters, such as gripper stiffness, damping, mould inertia, and excitation amplitude to the system dynamic characteristics. The results provide new insight and guidelines toward optimizing such mechanical systems.
A Coupled FEM/BEM for Fluid-Structure Interaction Using Ritz Vectors and Eigenvectors
Authors: Seybert A. F. , Wu T. W. , Li W. L.
Published: June 2008

In this paper, the finite element (FEM) and the boundary element method (BEM) are combined together to solve a class of fluid-structure interaction problems. The FEM is used to model the elastic structure and the BEM is used to model the acoustic fluid. Quadratic isoparametric elements are used in both the FEM and BEM models. Continuity conditions of pressure and normal velocity are enforced at the fluid-structure interface on which the normal vector is not required to be uniquely defined. An enhanced CHIEF formulation is adopted to overcome the nonuniqueness difficulty at critical frequencies. To reduce the dimension of the coupled structural acoustic equations, the structural displacement is approximated by a linear combination of either Ritz vectors or eigenvectors. An error norm and a participation factor are defined so that it is possible to evaluate the accuracy of a solution and to omit vectors with small participation factors. Example problems are solved to examine the accuracy of the numerical solutions and to compare the efficiency of the Ritz vector and eigenvector syntheses.
Plate Characteristic Functions and Natural Frequencies of Vibration of Plates by Iterative Reduction of Partial Differential Equation
Authors: Bhat R. B. , Singh J. , Mundkur G.
Published: June 2008

Natural frequency coefficients of rectangular plates and the corresponding plate characteristic functions are obtained by reduction of plate partial differential equation to an ordinary differential equation and solving it exactly. The reduction is carried out by assuming a deflection shape in one direction consistent with the boundary conditions and applying Galerkin’s averaging technique to eliminate the variable. The reduction method, commonly known as Kantorovich method, is applied sequentially on either directions of the plate and iterated until convergence is achieved for the natural frequency coefficients. The resulting plate characteristic functions are very good approximations to the normal modes of the plate. The results are tabulated for plates with combination of clamped, simply-supported, and free edge conditions.
Structural Modal Multifurcation With Internal Resonance: Part 2—Stochastic Approach
Authors: Ibrahim R. A. , Lee B. H. , Afaneh A. A.
Published: June 2008

Stochastic bifurcation in moments of a clamped-clamped beam response to a wide band random excitation is investigated analytically, numerically, and experimentally. The nonlinear response is represented by the first three normal modes. The response statistics are examined in the neighborhood of a critical static axial load where the normal mode frequencies are commensurable. The analytical treatment includes Gaussian and non-Gaussian closures. The Gaussian closure fails to predict bifurcation of asymmetric modes. Both non-Gaussian closure and numerical simulation yield bifurcation boundaries in terms of the axial load, excitation spectral density level, and damping ratios. The results of both methods are in good agreement only for symmetric response characteristics. In the neighborhood of the critical bifurcation parameter the Monte Carlo simulation yields strong nonstationary mean square response for the asymmetric mode which is not directly excited. Experimental and Monte Carlo simulation exhibit nonlinear features including a shift of the resonance peak in the response spectra as the excitation level increases. The observed shift is associated with a widening effect in the response bandwidth.
Identification of Certain Polynomial Nonlinear Structures by Adaptive Selectively-Sensitive Excitation
Authors: Ben-Haim Y.
Published: June 2008

This paper presents a method for identification of certain polynomial nonlinear dynamic systems by adaptive vibrational excitation. The identification is based on the concept of selective sensitivity and is implemented by an adaptive multihypothesis estimation algorithm. The central problem addressed by this method is reduction of the dimensionality of the space in which the model identification is performed. The method of selective sensitivity allows one to design an excitation which causes the response to be selectively sensitive to a small set of model parameters and insensitive to all the remaining model parameters. The identification of the entire system thus becomes a sequence of low-dimensional estimation problems. The dynamical system is modelled as containing both a linear and a nonlinear part. The estimation procedure presumes precise knowledge of the linear model and knowledge of the structure, though not the parameter values, of the nonlinear part of the model. The theory is developed for three different polynomial forms of the nonlinear model: quadratic, cubic and hybrid polynomial nonlinearities. The estimation procedure is illustrated through simulated identification of quadratic nonlinearities in the small-angle vibrations of a uniform elastic beam.
Digital Control Algorithms for Microgravity Isolation Systems
Authors: Sinha A. , Wang Y.-P.
Published: June 2008

New digital control algorithms have been developed to achieve the desired transmissibility function for a microgravity isolation system. Two approaches have been presented for the controller design in the context of a single degree of freedom system for which an attractive electromagnet is used as the actuator. The relative displacement and the absolute acceleration of the mass have been used as feedback signals. The results from numerical studies are presented. It has been found that the resulting transmissibility is quite close to the desired function. Also, the maximum coil currents required by new algorithms are smaller than the maximum current demanded by the previously proposed lead/lag method.
A Parameter Identification Method for the Rotordynamic Coefficients of a High Reynolds Number Hydrostatic Bearing
Authors: Rouvas C. , Childs D. W.
Published: June 2008

In identifying the rotordynamic coefficients of a high-Reynolds-number hydrostatic bearing, fluid-flow induced forces present a unique problem, in that they provide an unmeasureable and uncontrollable excitation to the bearing. An analysis method is developed that effectively eliminates the effects of fluid-flow induced excitation on the estimation of the bearing rotordynamic coefficients, by using power spectral densities. In addition to the theoretical development, the method is verified experimentally by single-frequency testing, and repeatability tests. Results obtained for a bearing are the twelve rotordynamic coefficients (stiffness, damping, and inertia coefficients) as functions of eccentricity ratio, speed, and supply pressure.
The Influence of Axial-Torsional Coupling on the Natural Frequencies of an Aerial Cable
Authors: Venkatasubramanian S. H. , White W. N.
Published: June 2008

The equations of motion for the small oscillations of a stranded, overhead transmission line are derived and linearized about the static equilibrium position. The influence of axial-torsional coupling on the natural frequencies is studied analytically and an expression is presented for the coupled natural frequency in torsion. In order to verify the analytical results, a finite element analysis of the linearized coupled differential equations is carried out. The results of each analysis are compared and show close agreement. The results of the zero coupling case also closely agree with previous work.
Natural Frequencies and Mode Shapes of Elliptic Plates With Boundary Characteristic Orthogonal Polynomials as Assumed Shape Functions
Authors: Rajalingham C. , Bhat R. B. , Xistris G. D.
Published: June 2008

The natural frequencies and natural modes of vibration of uniform elliptic plates with clamped, simply supported and free boundaries are investigated using the Rayleigh-Ritz method. A modified polar coordinate system is used to investigate the problem. Energy expressions in the Cartesian coordinate system are transformed into the modified polar coordinate system. Boundary characteristic orthogonal polynomials in the radial direction, and trigonometric functions in the angular direction are used to express the deflection of the plate. These deflection shapes are classified into four basic categories, depending on their symmetrical or antisymmetrical properties about the major and minor axes of the ellipse. The first six natural modes in each of the above categories are presented in the form of contour plots.
Scattering of Structural Waves by Nonlinear Elastic Joints
Authors: Vakakis A. F.
Published: June 2008

An analytic study of the scattering of structural waves by nonlinear elastic joints is presented. Under the assumption of small nonlinearities and/or amplitudes of motion, an averaging methodology is implemented for analyzing the interaction between an incident wave and a nonlinear joint with symmetric stiffness. It is found that, contrary to the predictions of existing linear theories, a single incident wave gives rise to an infinity of reflected waves with frequencies equal to odd multiples of the frequency of the incident wave. The orders of magnitude of the amplitudes of the various reflected waves are considered, and an application of the theory is made by considering the wave scattering from a joint with cubic stiffness nonlinearity. In addition, it is shown that the wave propagation approach presented in this work can be effectively used for predicting nonlinear free oscillations (standing waves) in finite waveguides with nonlinear joints.
Radiation from Bending Waves in the Presence of a Flow Boundary Layer
Authors: Akay A. , Ingard K. Uno
Published: June 2008

The effect of refraction by a flow boundary layer on the radiation of sound from a bending wave on a plate is investigated. Based on the relative velocities of the bending wave and the flow, four qualitatively different regimes are identified and results of numerical studies of radiation impedance and power emission are presented and discussed. For comparison, the role of a visco-thermal boundary layer is included with a correction of a numerical error in a previous paper.
Computation of the Eigenvalues of Wave Propagation in Periodic Substructural Systems
Authors: Williams F. W. , Wanxie Zhong , Bennett P. N.
Published: June 2008

The wave propagation constants of periodic structures are computed using the exact dynamic stiffness matrix of a typical substructure. The approach used is to show that wave propagation and the natural vibration eigenproblem are similar to such an extent that methods used to find the natural frequencies of a structure can be applied to find its wave propagation constants. The Wittrick-Williams algorithm has been incorporated into a finite element program, JIGFEX, in conjunction with exact dynamic member stiffnesses, to ensure that no phase propagation eigenvalues are missed during computation. The accuracy of the present approach is then demonstrated by comparing the results that it gives to analytically determined wave propagation curves for a Timoshenko beam on periodic simple supports. Finally, phase propagation curves are given for a complex Timoshenko beam structure of a type that would be very difficult to analyze analytically.
Vibration Signature Based Condition Monitoring of Bowl-Roller Coal Pulverizers
Authors: Nathan R. J. , Norton M. P.
Published: June 2008

The overall objective of the work reported in this paper is to minimize the cost of power generation in thermal power stations utilizing pulverized coal combustion processes for steam generation. The strategy of achieving this objective is based on an “on-condition maintenance” philosophy and vibration based diagnostic signature analysis techniques. The coal pulverizers reported on here are 783 RP (roll pressure) and 823 RP combustion engineering (CE) bowl-roller coal pulverizers (bowl mills) installed at the State Energy Commission of Western Australia (SECWA) power stations. This paper reviews the design philosophy, operational principles, and system dynamics and establishes the procedures for identifying the potential malfunction of bowl mills and their associated components. The influence of operating parameters, such as coal flow, primary air flow, and operating temperature, on mill vibration are investigated. The effects of journal spring force variation, such as magnitude, uneven spring force, and broken springs, are also studied. Special attention is also given to the diagnosis of the top radial bearing problem due to its remoteness from the bowl mill external structure. A spectral recovery technique utilizing the inverse frequency response function was developed for trend analysis and diagnostic purposes.
Transverse Natural Vibrations of a Cracked Beam Loaded with a Constant Axial Force
Authors: Krawczuk M. , Ostachowicz W. M.
Published: June 2008

The influence of transverse, one-edge open cracks on the natural frequencies of the cantilever beam subjected to vertical loads is analyzed. A finite element method (FE) is used for modelling the beam. A part of the cracked beam is modelled by beam finite elements with an open crack. Parts of the beam without a crack are modelled by standard beam finite elements. An algorithm of a linear stiffness matrix and a geometrical stiffness matrix calculation for a cracked element is presented. The results of numerical calculations obtained for the presented model are compared with the results of analytical calculations given in the literature and also with the results of numerical calculations obtained for a model with geometrical stiffness matrix of uncracked elements.