bluuebunny/crossref_metadata_2025 huggingface dataset:
Detection of Cracks in Rotating Timoshenko Shafts Using Axial Impulses
Authors: Collins K. R. , Plaut R. H. , Wauer J.
Published: June 2008

A rotating Timoshenko shaft with a single transverse crack is considered. The crack opens and closes during motion and is represented by generalized forces and moments. The shaft has simply supported ends, and the six coupled, piecewise-linear equations of motion (including longitudinal, transverse, and torsional displacements) are integrated numerically after application of Galerkin’s method with two-term approximations for each of the six displacements. Time histories and frequency spectra are compared for shafts with no crack and with a crack for which the crack depth is one-fifth of the shaft diameter. Free vibrations and the responses to a single axial impulse and periodic axial impulses are analyzed. The last case appears to provide an effective means for detecting cracks in rotating shafts.
The Extended Modal Reduction Method Applied to Rotor Dynamic Problems
Authors: Kane K. , Torby B. J.
Published: June 2008

In this paper, the existing Modal Reduction Method, which was developed to handle symmetric mass and stiffness matrices, is extended utilizing state-space formulation to handle nonsymmetric mass, damping, and stiffness matrices. These type of matrices typically accompany rotor dynamic problems since journal bearings supporting the rotor have nonsymmetric stiffness and damping characteristics. The purpose of modal reduction is to eliminate unimportant modes and degrees of freedom from the analytical model after they are found, so that further numerical analysis can be accelerated. The reduction described here leaves the retained eigenvalues and mode shapes unaltered from their original values. This method is demonstrated for a simple rotor problem having nonsymmetric system matrices including gyroscopic effects.
Unbalance Response of a Jeffcott Rotor Incorporating Long Squeeze Film Dampers
Authors: El-Shafei A.
Published: June 2008

The steady state unbalance response of a Jeffcott rotor incorporating long squeeze film dampers executing circular centered precession is obtained. Fluid inertia forces are included in the model of the squeeze film dampers, using an energy approximation. The fluid velocity profiles are assumed not to change much due to fluid inertia, and the kinetic coenergy of the fluid is calculated. The fluid inertia forces are then obtained by Lagrange’s equations in conjunction with Reynolds transport theorem. The unbalance response of the rotor is obtained by assuming circular centered precession, and it is shown that fluid inertia results in the excitation of a second mode for the Jeffcott rotor and decreases the useful range of vibration isolation of the dampers. It is also shown that the second mode can exhibit the jump resonance phenomenon.
Free Vibration Characteristics of Structures With Nonlinear Underlying Soil
Authors: Moustafa Kamal A. F. , El-Gebeily M.
Published: June 2008

Free vibration of structures is investigated by using a multidegree of freedom nonlinear model that allows for nonlinear behavior of the soil underlying the structure. The considered nonlinearity is due to the dependence of the soil shear modulus on vibration levels. The soil-structure interaction is modelled as nonlinear complex stiffness. The analysis is carried out by using mathematical perturbation theory. Modifications in the natural frequencies and existence of harmonics are demonstrated. The results are applied to an application example of massive deep water gravity structure.
Nonlinear Behavior of a Rotorcraft Model During Air Resonance
Authors: Flowers G. T. , Tongue B. H.
Published: June 2008

The term “air resonance” refers to an instability associated with helicopters in hover. It is characterized by a coupling between motions of the fuselage and the blades and is of primary concern for helicopters having soft in-plane rotors. This paper presents a study of the effects of nonlinearities on the dynamical behavior of a simplified air resonance model. In order to provide a direct comparison between the behavior of the linearized system and the nonlinear one, a linear analysis of the air resonance model is first performed. Then, the system is analyzed for the effect of selected nonlinearities on its steady state dynamical responses. Geometric nonlinearities and cubic lag damping are considered in these analyses.
Axisymmetric Free Vibration of Thick Orthotropic Hemispherical Shells Under Various Edge Conditions
Authors: Chao C. C. , Tung T. P. , Chern Y. C.
Published: June 2008

Axisymmetric free vibration of moderately thick polar orthotropic hemispherical shells are studied under the various boundary conditions with sliding, guided pin, clamped, and hinged edges. Based on the improved linear elastic shell theory with the transverse shear strain and rotatory inertia taken into account, the dynamic equlibrium equations are formulated and transformed into the displacement form in terms of mid-surface meridian and radial displacements and parallel circle cross-section rotation. These partial differential equations are solved by the Galerkin method using proper Legendre polynomials as admissible displacement functions with the aid of the orthogonality and a number of special integral relations. Natural frequencies and modes found from the eigenproblems are shown with reasonable results.
A Programmable Electromagnetic Bearing for Vibration Control of a Flexible Shaft
Authors: Bradfield C. D. , Roberts J. B. , Karunendiran S.
Published: June 2008

The transverse vibrations of flexible rotors can be reduced to safe levels by radial control forces at an intermediate span position, applied by a suitable actuator. One versatile control strategy applies forces proportional to displacement and velocity, with coefficients dependent on the rotational speed. This control can be realized with an electromagnetic bearing under microprocessor control. Suitable microprocessor software is described, to implement the required real-time computation of the control forces. Experimental results obtained from a test rig are compared with theoretical predictions. There are advantages in allowing the stiffness coefficient to become negative, provided that positive damping is simultaneously applied.
Test and Theory for Piezoelectric Actuator-Active Vibration Control of Rotating Machinery
Authors: Palazzolo A. B. , Lin R. R. , Alexander R. M. , Kascak A. F. , Montague J.
Published: June 2008

The application of piezoelectric actuators for active vibration control (AVC) of rotating machinery is examined. Theory is derived and the resulting predictions are shown to agree closely with results of tests performed on the air turbine driven-overhung rotor. The test results show significant reduction in unbalance, transient, and subsynchronous responses. Results from a 30 hour endurance test support the AVC system reliability. Various aspects of the electromechanical stability of the control system are also discussed and illustrated. Finally, application of the AVC system to an actual jet engine is discussed.
A Multi-Point Force Appropriation Method Based Upon a Singular Value Decomposition Approach
Authors: Juang Jer-Nan , Wright J. R.
Published: June 2008

Force appropriation methods aim to provide an estimate for the force pattern required to excite a “pure” normal mode in a vibration test where multiple exciters are available. In this paper, a new method based upon a Singular Value Decomposition approach is presented. The appropriated force vector which minimizes the in-phase response components while maximizing the required quadrature components is found, subject to a fixed force norm. The method can accommodate more transducers than exciters and also more exciters than effective degrees of freedom. The method is demonstrated upon a six degree of freedom theoretical model and it is shown that an estimate for the effective degrees of freedom can be obtained.
Prediction of Low Frequency Vibrational Frequencies of Submerged Structures
Authors: Everstine G. C.
Published: June 2008

Practical numerical techniques are described for calculating the low frequency vibrational resonances of general submerged structures. Both finite element and boundary element approaches for calculating fully-coupled added mass matrices are presented and illustrated. The finite element approach is implemented using existing structural analysis capability in NASTRAN. The boundary element approach uses the NASHUA structural acoustics program in combination with NASTRAN to compute the added mass matrix. The two procedures are compared in application to a submerged cylindrical shell with flat end closures. Both procedures proved capable of computing accurate submerged resonances; the more elegant boundary element procedure is easier to use but may be more expensive computationally.
Force Reconstruction for Impact Tests
Authors: Bateman V. I. , Carne T. G. , Gregory D. L. , Attaway S. W. , Yoshimura H. R.
Published: June 2008

Two force reconstruction techniques were used to evaluate the impact test of a scale model nuclear transportation cask dropped 30 ft. onto an unyielding target. The two techniques are: the sum of weighted acceleration technique (SWAT) and the deconvolution technique (DECON). A brief description and the calibration of the techniques as applied to the cask are presented. For the impact test, both techniques yielded very similar resultant forces and provided more accurate definition of the force-time history for the cask than is available from conventional data reduction methods. An applied moment, measurement previously unobtainable from conventional accelerometer data reduction techniques, was determined with SWAT. The angular velocity calculated with SWAT was verified with photometric measurements.
A Method for Substructural Sensitivity Synthesis
Authors: Heo Joo Ho , Ehmann K. F.
Published: June 2008

A new method, termed the substructural sensitivity synthesis method, which utilizes the computational merits of the component mode synthesis technique was proposed for the simple calculation of design sensitivities of the dynamic characteristics of substructurally combined structures. It has been shown that the modal sensitivities of the entire structure can be obtained by synthesizing the substructural modal data and the sensitivities of the modal data for the design variables of the modifiable substructure. For a truss structure, as an example, the sensitivities of the eigenvalues and eigenvectors obtained by the new method were compared with exact solutions in terms of accuracy and computational efficiency.
Centrifugal-Acceleration Modes for Incompressible Fluid in the Leakage Annulus Between a Shrouded Pump Impeller and Its Housing
Authors: Childs D. W.
Published: June 2008

An analysis is presented for the perturbed flow in the leakage path between a shrouded-pump impeller and its housing. A bulk-flow model is used for the analysis consisting of the path-momentum, circumferential-momentum, and continuity equations. Shear stress at the impeller and housing surfaces are modeled according to Hirs’ turbulent lubrication model. The governing equations have been used earlier to examine rotordynamic reaction forces developed by lateral and axial impeller motion. A perturbation expansion of the governing equations in the eccentricity ratio yields a set of zeroth and first-order governing equations. The zeroth-order equations define the leakage rate, and the velocity and pressure distributions for a centered impeller position. The first-order equations define the perturbations in the velocity and pressure distributions due to axial or lateral motion of the impeller. Prior analyses by the author of the perturbation equation have examined the reaction forces on the shroud due to rotor motion. These analyses have produced “resonance” phenomena associated with the centrifugal-acceleration body forces in the fluid field. In the present analysis, an algorithm is developed and demonstrated for calculating the complex eigenvalues and eigenvectors associated with these resonances. First-and second-natural-frequency eigensolutions are presented for mode shapes corresponding to lateral excitation. First-natural-frequency eigensolutions are also presented for mode shapes corresponding to axial excitation.
Identification of a Nonproportional Damping Matrix from Incomplete Modal Information
Authors: Minas C. , Inman D. J.
Published: June 2008

In modeling structures the damping matrix is the most difficult to represent. This is even more difficult in complicated structures that are not lightly damped. The work presented here provides a method of modeling the damping matrix of a structure from incomplete experimental data combined with a reasonable representation of the mass and stiffness matrices developed by finite element methods and reduced by standard model reduction techniques. The proposed technique uses the reduced mass and stiffness matrices and the experimentally obtained eigenvalues and eigenvectors in a weighted least squares or a pseudo-inverse scheme (depending on the number of the equations that are available) to solve for the damping matrix. The results are illustrated through several examples. As an indication of the accuracy of the method, fictitious examples where the damping matrix is originally known are considered. The proposed method identifies the exact viscous or hysteretic damping matrix by only using a partial set, half of the system’s eigenvalues and eigenvectors. The damping matrix is assumed to be real, symmetric, and positive semidefinite.
Friction Damping of Circular Motion and Its Implications to Vibration Control
Authors: Griffin J. H. , Menq C.-H.
Published: June 2008

When vibrating bodies are mutually constrained through friction contact they may move with respect to each other and dissipate energy at the interface. If the relative motion of the contacting surfaces follows a straight line the motion is said to be one-dimensional. This case has been examined extensively in the literature. More generally the point of contact can follow a path which is not a straight line. For the case of a periodic response the path will form a closed loop. In this paper we investigate the simplest, yet most extreme case of two dimensional motion—when the contacting point moves in a circular path. It is found that an exact solution can be derived for the problem of a frictionally constrained system when it is subjected to a circular excitation. The solution is used to determine the characteristics of the system’s response and they are compared with those for one-dimensional motion. In the case of one-dimensional motion if the contacting surfaces are compliant they will stick for at least a portion of each cycle. This is not the case for circular motion as it is found that the interface is either always stuck for small motions or always slipping if the excitation is above a certain level. This result suggests that the slip/stick transition which occurs during every cycle for the one-dimensional case may not be as important for the more general two-dimensional friction contact problem. Friction is often a major source of energy dissipation in vibrating machinery. As a result, the friction contact is sometimes used to reduce the peak response of the system by designing the contacting parts so as to have an optimum friction constraint. In order to investigate this effect expressions are derived for the peak amplitude as a function of the friction force, for the friction force that will minimize peak response, and for the amplitude of the peak response under optimum friction conditions. The results for circular motion are compared with those for straight line motion in order to assess the importance of two-dimensional effects.
Transient Waves in Anisotropic Laminated Plates, Part 1: Theory
Authors: Liu G. R. , Tani J. , Ohyoshi T. , Watanabe K.
Published: June 2008

A hybrid numerical method in which the finite element method and the method of Fourier transforms are combined is proposed for computing the transient waves in anisotropic laminated plates excited by impact loads. The anisotropic laminated plate is divided into N plate elements, and the principle of virtual work is used to develop approximate dynamic equilibrium equations for three- and two-dimensional problems. The displacement response is determined by employing the Fourier transformation and the modal analysis. This hybrid numerical method is straightforward and easy to use.
Transient Waves in Anisotropic Laminated Plates, Part 2: Application
Authors: Liu G. R. , Tani J. , Ohyoshi T. , Watanabe K.
Published: June 2008

The application of the hybrid numerical method proposed in the previous paper by the present authors to the computation of transient waves in composite material plates excited by step-impact loads is presented in this paper. Both the two-dimensional problem (line step-impact load) and the three-dimensional problem (point step-impact load) are considered. First, the displacement responses of isotropic plates are computed by using the hybrid numerical method and the results are compared with those obtained by the method of the head of the pulse approximation and the method of generalized rays. Next, the displacement responses of a hybrid composite laminated plate excited by a line step-impact load and a point load are calculated, and some interesting results are obtained.
Rotordynamic Coefficients for Partially Roughened Pump Annular Seals
Authors: Scharrer J. K. , Nelson C. C.
Published: June 2008

The basic equations are derived for incompressible flow in an annular seal with partially roughened surfaces. The flow is assumed to be completely turbulent in the axial and circumferential directions with no separation, and is modeled by Hirs’ turbulent lubrication equations. Linearized zeroth and first-order perturbation equations are developed for small motion about a centered position by an expansion in the eccentricity ratio. The zeroth-order continuity and momentum equations are solved numerically, yielding the axial and circumferential velocity components and the pressure distribution. The first-order equations are reduced to three linear, complex, ordinary, differential equations in the axial coordinate Z. The equations are integrated to satisfy the boundary conditions and yield the perturbated pressure distribution. This resultant pressure distribution is integrated along and around the seal to yield the force developed by the seal from which the corresponding dynamic coefficients are derived. The results of a parametric study on the effect of the rough length/smooth length ratio on the seal leakage and rotordynamic coefficients are presented.
Sound Transmission in a Duct With an Array of Lined Resonators
Authors: Trochidis A.
Published: June 2008

A simple method is presented for describing the sound transmission in a duct containing an array of lined resonators. The impedance of a resonator element is calculated, including the effect of the lining and the duct is modeled as a one-dimensional waveguide with lumped impedances. An expression for the TL is derived from considerations of pressure and mass flow continuity along the duct. Experimental data compared to numerical computations show that the method developed here describes satisfactorily the performance of the duct and allows useful parametric analyses which can lead to improved design.
An Eigenvalue Based Acoustic Impedance Measurement Technique
Authors: Hull A. J. , Radcliffe C. J.
Published: June 2008

A method is developed for measuring acoustic impedance. The method employs a one-dimensional tube or duct with excitation at one end and an unknown acoustic impedance at the termination end. Microphones placed in the tube are then employed to measure the frequency response of the system from which acoustic impedance of the end is calculated. This method uses fixed instrumentation and takes advantage of modern Fast Fourier Transform analyzers. Conventional impedance tube methods have errors resulting from movement of microphones to locate the maxima and minima of the wave pattern in the impedance tube or require phase matched microphones with specific microphone spacing. This technique avoids these problems by calculating the acoustic impedance from measured duct eigenvalues. Laboratory tests of the method are presented to demonstrate its accuracy.
Wall Pressure Fluctuations During Transition on a Flat Plate
Authors: Gedney C. J. , Leehey P.
Published: June 2008

Detailed measurements of wall pressure fluctuations have been made in the intermittent (laminar-turbulent) region of a flat plate boundary layer. Digital sampling and processing techniques were used. The properties of these pressure fluctuations were found to be similar to the previous measurements made in the fully turbulent region. The measurements were repeated with a single two-dimensional surface roughness on the plate. The only changes in the results were a decrease in the transition Reynolds number from 2 × 106 to 1.6 × 106, and an increase in the decay rate of the longitudinal cross-spectral density magnitude by a factor of about 1.5. Emmons’ (1951) analytical model was applied for two cases: (1) a constant source density downstream of transition and, (2) a line source distribution at transition. Both predicted burst rates as functions of intermittency appreciably higher than measured values. Wall pressure spectra scaled on dynamic head showed a strong dependency on intermittency. This dependency was largely resolved, at least for intermittencies greater than 64 percent, by scaling on turbulent mean shear stress at the wall.
Sound Radiation From a Finite Cylindrical Shell Covered With a Compliant Layer
Authors: Laulagnet B. , Guyader J. L.
Published: June 2008

The aim of this work is to present the mathematical analysis and numerical results about sound radiation from a finite cylindrical shell covered with a compliant layer, immersed in water. The shell motion is obtained using Flu¨gge’s operator whereas the layer is described by a locally reacting material. The results are presented both in shell radial quadratic velocity and radiated power. Two major conclusions can be drawn when looking at results: (1) a reasonable stiffness layer allows one to reduce the radiated power in a large frequency domain; (2) the layer has a strong influence on the shell velocity which exhibits an antiresonance phenomenon when covered.
Dynamic Response of a Cylindrical Shell Panel to Explosive Loading
Authors: Redekop D. , Azar P.
Published: June 2008

The dynamic response of steel cylindrical shell panels subjected to external free-field air-blast loading is investigated. The cases of rectangular and square panels having hinged and immovable boundary conditions are considered. Approximate theoretical solutions are presented for linear and nonlinear geometric behavior. Numerical solutions are given for linear, nonlinear geometric and general nonlinear behavior. Results from the theoretical and numerical solutions are compared for several panel rise cases, and conclusions are drawn.
Random Response of Thick Laminated Rectangular Plates
Authors: Srinivasan R. S. , Krishnan P. A.
Published: June 2008

The present paper deals with the random response analysis of clamped thick laminated rectangular plates subjected to white noise excitation. The refined plate theory postulated by Reddy has been used. The analysis has been done using an integral equation technique. The random response results obtained for istropic square plates based on different plate theories (viz.) classical theory, first order theory and refined theory, have been compared. A parametric study has been conducted for angle ply and cross ply plates by varying the lay up of layers and a/h ratios.
Analysis of Nonrepeatable Radial Vibration of Magnetic Disk Spindles
Authors: Ono K. , Saiki N. , Sanada Y. , Kumano A.
Published: June 2008

The nonrepeatable radial vibration (NRRV) of spindle motors used in magnetic disk memory devices was studied in detail. In particular a theoretical and experimental investigation on the comparison of NRRV in time and frequency domains was conducted. The random and statistical characteristics of NRRV were ascertained by analyzing the amplitude distributions of both asynchronous and synchronous vibration components in the frequency domain. It was found that the main part of NRRV is composed of asynchronous components in most of the spindles tested. Some of the asynchronous component amplitudes, varying randomly, can be approximated by Rayleigh distribution function. It was also found that the synchronous vibrations include nonrepeatable components. The variance of NRRV measured in the time domain was shown theoretically and experimentally to be equal to the sum of the total power of asynchronous components and the total variance of synchronous components. From this relation, the cause of tracking error in such memory devices can be analyzed quantitatively in frequency domain.
A Hybrid Approach to Test-Analysis-Model Development for Large Space Structures
Authors: Kammer D. C.
Published: June 2008

A new finite element model (FEM) reduction method is presented for use in the generation of Test-Analysis-Models (TAM) in test-analysis correlation. The method addresses the concern that some current TAM methodologies, specifically the Modal TAM, are overly sensitive to differences between test mode shapes and analysis mode shapes. This sensitivity can result in large off-diagonal terms within the orthogonality and cross-orthogonality matrices used for test-analysis mode shape correlation. It has been hypothesized that the sensitivity is due to the Modal TAM’s poor representation of residual mode shapes and frequencies which are modes that are not targeted for identification. In many cases it has been observed that the less accurate static TAM often gives better off-diagonal correlation results. A new Hybrid TAM methodology is developed to combine the exact representation of the FEM target modes from the Modal TAM with the more accurate static TAM representation of the residual modes. The superior residual dynamics representation of the Hybrid TAM is demonstrated for both a simple spacecraft and a much more detailed representation of a Large Space Structure. Simulated test-analysis correlation results are presented for both examples where test mode shapes are represented by FEM target modes with noise modeled as a random linear combination of all FEM modes. Analysis indicates that the Hybrid TAM’s improved residual representation results in reduced sensitivity of the test-analysis correlation to model error.
Recursive Identification of Vibrating Structures from Noise-Corrupted Observations, Part 1: Identification Approaches
Authors: Ben Mrad R. , Fassois S. D.
Published: June 2008

In this paper the problem of recursive structural dynamics identification from noise-corrupted observations is addressed, and approaches that overcome the weaknesses of current methods, stemming from their underlying deterministic nature and ignorance of the fact that structural systems are inherently continuous-time, are introduced. Towards this end the problem is imbedded into a stochastic framework within which the inadequacy of standard Recursive Least Squares-based approaches is demonstrated. The fact that the continuous-time nature of structural systems necessitates the use of compatible triples of excitation signal type, model structure, and discrete-to-continuous transformation for modal parameter extraction is shown, and two such triples constructed. Based on these, as well as a new stochastic recursive estimation algorithm referred to as Recursive Filtered Least Squares (RFLS) and two other available schemes, a number of structural dynamics identification approaches are formulated and their performance characteristics evaluated. For this purpose structural systems with both well separated and closely spaced modes are used, and emphasis is placed on issues such as the achievable accuracy and resolution, rate of convergence, noise rejection, and computational complexity. The paper is divided into two parts: The problem formulation, the study of the interrelationships among excitation signal type, model structure, and discrete-to-continuous transformation, as well as the formulation of the stochastic identification approaches are presented in the first part, whereas a critical evaluation of their performance characteristics based on both simulated and experimental data is presented in the second.
Recursive Identification of Vibrating Structures from Noise-Corrupted Observations, Part 2: Performance Evaluation via Numerical and Laboratory Experiments
Authors: Ben Mrad R. , Fassois S. D.
Published: June 2008

In the first part of this paper (Ben Mrad and Fassois, 1991), the problem of recursive structural dynamics identification from noise-corrupted observations was examined, and six approaches that properly account for the presence of noise in the experimental data and the fact that structural systems are inherently continuous-time were formulated. In this second part the relative performance characteristics of these approaches are investigated by using numerically simulated and laboratory data, the latter obtained from a free-free beam experiment. Structural systems with well separated and closely spaced modes are considered, and emphasis is placed on issues such as the achievable accuracy and resolution, rate of convergence, noise rejection, computational complexity, the need for model overdetermination, and the distinction of structural from “computational” vibrational modes. Unlike alternative methods, when properly used, the proposed approaches are shown to offer good performance with data corrupted at various noise-to-signal ratios.
Active Control for Vibration Suppression in a Flexible Beam Using a Modal Domain Optical Fiber Sensor
Authors: Cox D. E. , Lindner D. K.
Published: June 2008

In this paper we discuss the use of a modal domain optical fiber sensor (MD sensor) as a component in an active control system to suppress vibrations in a flexible beam. An MD sensor consists, roughly, of a laser source, an optical fiber, and detection electronics. The basic operating principles of this sensor are reviewed and a model of this sensor is derived. It is shown that the output of an MD sensor is proportional to the integral of the axial strain along the optical fiber. Since we use a significant length of fiber for sensing, this sensor is called a distributed-effect sensor. When an MD sensor is attached to, or embedded in, a flexible structure, it will sense the strain in the structure along its gage length. Here we integrate the sensor model into the model for a flexible structure. Based on this system model, a control system with a dynamic compensator is designed to add damping to the low order modes of the flexible structure. To verify the modeling procedure an experiment was conducted. The experimental setup consisted of a cantilevered beam with a piezoelectric actuator and an MD sensor. A simulation of the experiment was developed based on the component models. It is shown that experimental responses closely match simulated responses for both open loop and closed loop tests. The experiment also incorporated several recent advances for practical MD sensor implementation including lead-in/lead-out insensitive fibers and elliptical core sensing fiber.
Viscoelastic Circular Plate Wave Guide Absorber
Authors: Hettema C. D. , Shin Y. S. , Kim K. S.
Published: June 2008

A waveguide absorber removes and dissipates vibrational energy from a structure by traveling waves. The performance of a wave guide absorber is determined by the driving point impedance. In this study a viscoelastic circular plate waveguide absorber is developed and it is shown that the driving point impedance of the viscoelastic wave guide absorber can be theoretically predicted using a Mindlin type plate theory. To validate the results of this study, viscoelastic circular plates were tested to determine their driving point impedance.
A Boundary Element Approach to Optimization of Active Noise Control Sources on Three-Dimensional Structures
Authors: Cunefare K. A. , Koopmann G. H.
Published: June 2008

This paper presents the theoretical development of an approach to active noise control (ANC) applicable to three-dimensional radiators. The active noise control technique, termed ANC Optimization Analysis, is based on minimizing the total radiated power by adding secondary acoustic sources on the primary noise source. ANC Optimization Analysis determines the optimum magnitude and phase at which to drive the secondary control sources in order to achieve the best possible reduction in the total radiated power from the noise source/control source combination. For example, ANC Optimization Analysis predicts a 20 dB reduction in the total power radiated from a sphere of radius α at a dimensionless wavenumber ka of 0.125, for a single control source representing 2.5 percent of the total area of the sphere. ANC Optimization Analysis is based on a boundary element formulation of the Helmholtz Integral Equation, and thus, the optimization analysis applies to a single frequency, while multiple frequencies can be treated through repeated analyses.
An Acoustic Variational Principle and Component Mode Synthesis Applied to the Analysis of Acoustic Radiation from a Concentrically Stiffened Plate
Authors: Ginsberg J. H. , McDaniel J. G.
Published: June 2008

This study concerns the effects of circumferential ring stiffeners on the vibration and acoustic radiation of a submerged circular elastic plate supported by an infinite rigid baffle. The analysis employs variational principles, in which surface pressure and velocity are represented by assumed modal functions. It is shown that the use of a Fourier series expansion of the Green’s function, along with Bessel function pressure modes, greatly simplifies computation of the fluid-structure interaction. Two structural formulations are addressed, differing by whether the connection between the plate and stiffeners is implicitly or explicitly enforced. The results for surface response are used in conjunction with the Kirchhoff-Helmholtz integral theorem to evaluate near- and farfield pressures. An example of a single stiffener illustrates the influence of stiffener location on radiated power.
Linear Waves in Bubbly Liquids via the Kramers-Kronig Relations
Authors: Brauner N. , Beltzer A. I.
Published: June 2008

A simple closed form analytic solution, as well as numerical solutions, are derived for acoustic waves of an arbitrary frequency, propagating in dilute bubbly liquids. The applied method treats the effective wave as a causal response of a linear system. The results are compared with the prediction of Foldy’s theory, which in this particular case is shown to be consistent with the Kramers-Kronig relations. These results thus complement recently reported investigations concerning the causal approach as well as the validity of Foldy’s theory.
A Note on Pole Placement of Mechanical Systems
Authors: Minas C. , Inman D. J.
Published: June 2008

An output feedback method is developed, that systematically places a desired number of poles of a closed-loop system at or near desired locations. The system is transformed to its equivalent controllable canonical form, where the output feedback gain matrix is calculated in a weighted least squares scheme, that minimizes the change of the remaining modes of the system. The advantage of this method over other pole placement routines is the fact that the influence on the remaining unplaced modes of the system is minimum, which is particularly important in preserving closed-loop stability.
Dynamic Analysis and Control of a Double-Carriage Rotary Actuator for Accurate Magnetic Disk Head Positioning
Authors: Kakizaki T. , Mizukami M. , Kogure K.
Published: June 2008

Dynamic analysis and control for accurate magnetic disk head positioning using a compact double-carriage rotary actuator is presented. Rolling mode vibration, due to a small dynamic imbalance in the head arm carriage, is one of the major factors in positioning servo instability. To avoid such vibration, structural symmetry should be maintained along the actuator pivot axis. Vibration interaction in the double-carriage rotary actuator is also clarified by mathematical modeling of a disk drive. The positioning error due to the interaction is reduced by one-third to the submicron order, even during very high-speed accessing, by a cross-feedforward decoupling control using a precompensator based on the model.
Prediction of Rotating Blade Modes from Measured Nonrotating Modal Parameters
Authors: Chou Yuan-Fang , Yeh Wern-Cheng
Published: June 2008

The method presented in this paper can predict the modal parameters of a rotating blade accurately via the easily measured modal parameters of the blade in the nonrotating state. The derivation of the eigenvalue problem in nonrotating modal coordinates is based on the continuum model of general linear elastic solids such that it can be applied to complex real structures. Therefore, the modal parameters for different rotating speeds can be found without testing the blade under each different rotating speed. Experiments were conducted to check the proposed method. The results showed that the predicted characteristics were in good agreement with the measured characteristics.
Power Flow and Energy Balance Between Nonconservatively Coupled Oscillators
Authors: Chen Genda , Soong T. T.
Published: June 2008

The concept of power flow, which has been found to be a powerful tool in the dynamic analysis of complex systems with conservative connecting elements, is extended to the case of nonconservatively coupled mechanical or structural systems. In order to avoid any ambiguity in the definition of power flow in this situation, the nonconservatively coupled oscillators are considered as a limiting case of oscillators with conservative connections. Through the introduction of dissipative power and penetrating power flow, this approach is shown to produce a physical consistent formulation. Some important and distinguishing properties of this formulation are demonstrated and discussed through numerical examples.
Effect of Radial Thickness on the In-Plane Free Vibrations of Circular Annular Discs
Authors: Singal R. K. , Williams K. , Wang H.
Published: June 2008

In this paper the in-plane free vibrations of both thick and thin circular annular discs are studied. The well-known energy method, which is based on the three-dimensional theory of elasticity, is used in the derivation of the frequency equation of the disc. The frequency equation yields all the natural frequencies for all the circumferential modes of vibration, including the breathing and beam-type modes. In order to assess the validity of the analysis experimental data were acquired on several models. The paper first describes briefly the energy method analysis, this is followed by a description of the various experimental models. Finally, the calculated values of frequencies are compared with the experimental values. A very close agreement between both the theoretical and experimental values of the resonant frequencies for all the models was obtained and this validates the energy method of analysis.
Dual Active and Passive Control of Large Flexible Structures
Authors: Pan T. S. , Rao S. S. , Venkayya V. B.
Published: June 2008

A unified passive damping design algorithm, using active control design techniques and least squares method, is developed to improve the stability and performance of closed-loop controlled structures. To achieve the stringent requirements of large flexible structures (LFS), dual active/passive control using interacting substructure decentralized control and unified passive damping design method is introduced. Physical coordinates are used in modeling; since no modal data is used, no modal errors are involved in the modeling process. Examples are presented to illustrate the design procedures and their effectiveness.
Shaft Finite Elements for Rotor Dynamics Analysis
Authors: Gmu¨r T. C. , Rodrigues J. D.
Published: June 2008

This paper presents efficient C0-compatible finite elements for the modelling of rotor-bearing systems. The proposed linearly tapered elements, which have a variable number of nodal points, are simple and attractive from a cost viewpoint. They include the effects of translational and rotatory inertia, gyroscopic moments, internal viscous and hysteretic damping, shear deformations, and mass eccentricity. Developed from the weak formulation associated with the differential equations governing the transverse dynamic behavior of rotors, these elements show a convergence pattern similar to the one obtained with conventional C1-compatible shaft elements. Numerical examples are provided, which compare the proposed approach to the C1-formulation or to previously published results.
A Unified Approach for the Dynamics of Beams Undergoing Arbitrary Spatial Motion
Authors: Boutaghou Z.-E. , Erdman A. G.
Published: June 2008

A unified approach to systematically derive the dynamic equations for flexible bodies is proposed. This approach is not limited to a particular definition of the field of kinematic representation of deformation. Dynamics of flexible bodies in arbitrary spatial motion experiencing small and large elastic deflections are considered. Two test cases are analyzed via the unified approach. For the first case, linear partial differential equations based on the Euler-Bernoulli beam theory with the von Ka´rma´n geometric constraint for flexible bodies in planar motion are derived. These equations capture the centrifugal stiffening effects arising in fast rotating structures. For the second case, analytical and numerical evidence of out-of-plane vibrations of an in-plane rotating three-dimensional Timoshenko beam with cross sectional area of arbitrary shape is reported.
Centrifugal Pendulum Vibration Absorbers—Theory and Practice
Authors: Mitchiner R. G. , Leonard R. G.
Published: June 2008

Reciprocating mechanical systems, such as pumps and compressors, present a nonuniform dynamic load to the driving motor. These load variations and their interactions with the dynamic characteristics of the motor result in dynamic torque variations on the rotor which have very significant harmonic components. These torque variations contribute to undesirable dynamic loading of the mounting frame and subsequent transmission of vibrations and noise into the supporting structure. Centrifugal pendulum absorbers offer an excellent means for the elimination of the effects of some of these torque harmonics. Since most reciprocating machinery operates over a speed range depending on load conditions, the centrifugal absorber is an excellent means for insuring that the suppression of vibrations is insensitive to speed and local conditions. While the virtues of centrifugal absorbers are well known as are the differential equations describing the dynamics of the absorbers, the literature does not address the case of real absorbers with distributed mass properties. This paper presents a derivation of the equations of motion for the rotor and the distributed mass pendulum, along with those insights and techniques necessary for the practical design of a centrifugal pendulum system. The tuning of the pendulum is discussed along with damping requirements. A case study is presented where a set of pendulums is employed on the rotor of an air compressor driven by a close-coupled electric induction motor. In the case study, first and second harmonic rotor torques (30 percent and 9 percent, respectively, of the average rotor torque) are eliminated with 3.77 lb and 0.83 lb pendulums in a 3-horsepower, 875 rpm machine.
Active Control of High Order Acoustical Modes in a Semi-Infinite Waveguide
Authors: Stell J. D. , Bernhard R. J.
Published: June 2008

This paper presents an analysis of the effectiveness of active noise control methods for control of high order modes in rigid-walled, semi-infinite waveguides. The waveguides examined in this investigation are terminated at one end with a rigid end. The case studies performed reconfirmed that n control actuators can control n propagating modes (including the plane wave) in a waveguide if the actuators are properly placed. The results also confirmed that the control actuators should be located at the node surfaces of the most significant evanescent modes to avoid various problems that evanescent modes cause active control systems. A significant new finding is the effect of the rigid waveguide termination on the active controller. The reflected energy from the termination causes standing waves in the region between the rigid termination and the secondary sources. At certain frequencies which correspond to resonant conditions, the standing wave amplitudes become large and the control actuator strength must be high. At these frequencies the effects of the evanescent modes become significant even when the mode is not close to its cut-on frequency. Similar resonant effects can be expected to affect active noise control performance for any case where there are significant reflections in the waveguide upstream of the control actuators.
Use of the Generalized Impulse Momentum Equations in Analysis of Wave Propagation
Authors: Gau Wei-Hsin , Shabana A. A.
Published: June 2008

A procedure is developed in this paper to study the propagation of impact-induced axial waves in constrained beams that undergo large rigid body displacements. The solution of the wave equations is obtained using the Fourier method. Kinematic conditions that describe mechanical joints in the system are formulated using a set of nonlinear algebraic constraint equations that are introduced to the dynamic formulation using the vector of Lagrange multipliers. The initial conditions which represent the jump discontinuity in the elastic coordinates as the result of impact are predicted using the generalized impulse momentum equations that involve the coefficient of restitution as well as the Jacobian matrix of the kinematic constraints. The convergence of the series solutions presented in this paper is examined and the analytical and numerical results are found to be consistent with the solutions obtained by the use of the classical theory of elasticity in the case of plastic impact. The cases in which the coefficient of restitution is different from zero are also examined and it is shown that the generalized impulse momentum equations can be used with confidence to study the propagation of elastic waves in applications related to multibody dynamics.
General Solution of Acoustic Wave Equation for Circular Reversing Chamber with Temperature Gradient
Authors: Kim Yang-Hann , Choi Jae Woong
Published: June 2008

A general solution for transmission loss in a circular reversing chamber with the effects of temperature gradient, offset, and twisting angle variations of inlet/outlet ports is obtained by using the mode matching technique. The assumptions included in the solution method are division of the reversing chamber into segments, continuity of pressure and velocity at the boundaries of adjacent elements, constant temperature along each segment, and rigid wall boundary condition. Furthermore, the general solution can reduce to the existing solution of acoustic wave equation for a reversing chamber when no mean flow of exhaust gas and temperature gradient are present. The numerical simulation results based upon the obtained governing equation have the same trough frequencies and shapes of transmission loss curves as the experimental results performed on various types of reversing chambers. From these simulations, it is determined that the diameter of the reversing chamber dictates that cutoff frequencies in the transmission loss curves, and its length controls the number of standing waves in the chamber. Reversing chambers exhibit the acoustic characteristics of simple expansion chambers when the ratios of length over diameter are small. Even for limiting cases, i.e., Helmholtz resonators and close ended pipes, simulations produce the predicted results derived by other existing theories for silencers.