bluuebunny/crossref_metadata_2025 huggingface dataset:
A Method to Determine the Boundary Conditions of the Finite Element Model of a Slender Beam Using Measured Modal Parameters
Authors: Fengquan Wang , Shiyu Chen
Published: February 2008

In this paper, a method used to determine the boundary conditions of the Finite Element Model of a slender beam with measured structure modal parameters is presented. On deriving the method, the finite element model theory for dynamic calculating is used. Combined with the modal parameters from experiment, an FEM-modal parameter equation to determine the boundary conditions is put forward. For solving the equation, three methods are given. The first is the accurate method. The second is the full mode computation method by means of generalized inverse matrix. The third is the interpolation method of frequency. A numerical simulation with computer is given and the results of calculation fully verify the effectiveness of the method offered and also verify that the accuracy of the method is satisfying. Finally, an applied example is given and the results of calculation fully verify the effectiveness of the method offered.
Muffler Performance Studies Using a Direct Mixed-Body Boundary Element Method and a Three-Point Method for Evaluating Transmission Loss
Authors: Wu T. W. , Wan G. C.
Published: February 2008

In this paper, a single-domain boundary element method is presented for muffler analysis. This method is based on a direct mixed-body boundary integral formulation recently developed for acoustic radiation and scattering from a mix of regular and thin bodies. The main feature of the mixed-body integral formulation is that it can handle all kinds of complex internal geometries, such as thin baffles, extended inlet/outlet tubes, and perforated tubes, without using the tedious multi-domain approach. The variables used in the direct integral formulation are the velocity potential (or sound pressure) on the regular wall surfaces, and the velocity potential jump (or pressure jump) on any thin-body or perforated surfaces. The linear impedance boundary condition proposed by Sullivan and Crocker (1978) for perforated tubes is incorporated into the mixed-body integral formulation. The transmission loss is evaluated by a new method called “the three-point method.” Unlike the conventional four-pole transfer-matrix approach that requires two separate computer runs for each frequency, the three-point method can directly evaluate the transmission loss in one single boundary-element run. Numerical results are compared to existing experimental data for three different muffler configurations.
Asymptotic Analysis of the Torsional Vibrations in Reciprocating Machinery
Authors: Ashrafiuon H. , Whitman A. M.
Published: February 2008

A class of two degree of freedom reciprocating machines is analyzed and simple asymptotic expressions for both the steady state and transient vibration levels are obtained. The results are compared with those of a standard numerical modeling package, and are found to be in good agreement for parameter values typical of real machines. This happens because real machines are designed so that the vibration levels are small, thereby satisfying the conditions for the validity of the approximation.
Development of an Electrically Controllable Damper Using a Liquid Crystal
Authors: Morishita S.
Published: February 2008

This paper describes a new electrically controllable damper that uses a liquid crystal (LC) as the working fluid. LC is a homogeneous organic liquid characterized by the long-range order of its molecular orientation. The sample LC used in this work is a thermotropic, low molecular-weight LC which appears in the nematic phase, and was originally developed for display devices. The molecular orientation of the nematic phase is characterized by slender ellipsoidal shape molecules, the main axis of which can be controlled by applying an electric or magnetic field. When an electric field is applied to a LC, the orientation order of the molecules becomes parallel to the applied electric field, causing the apparent viscosity to increase. This phenomenon is known as the electroviscous effect. To study the application of the electroviscous effect of a LC to a controllable mechanical damping device, a prototype controllable damper was constructed and its performance was examined. In this damper, a piston, equipped with several concentric cylindrical electrodes attached to the piston rod, moves in the liquid crystal. During the reciprocal movement of the electrodes, LC flow through the electrodes is controlled by applying electric voltage to the latter. Damper performance was investigated under various DC electric field strengths, piston oscillation amplitudes and frequencies. The results show that the controllable damping force was three times larger with the application of an electric field than that without, and that the range of force variation was kept at the same level regardless of the frequency and amplitude of piston motion.
Revisiting the Moving Mass Problem: Onset of Separation Between the Mass and Beam
Authors: Lee U.
Published: February 2008

In the moving mass problem, the interaction force between a moving mass and structure obviously depends on the velocity of moving mass and the flexibility of structure. Thus, in some situations, the interaction force may become zero to change its sign, which implies the onset of the separation between the moving mass and structure. Most investigations on this subject have missed or ignored the possibility of the onset of separation in solving the dynamic responses of structures excited by moving masses. Hence, this paper investigates the onset of the separation between the moving mass and beam, and then takes into account its effect in calculating the interaction forces and also in calculating the dynamic responses of the beams considered herein. It is shown that the separation between the moving mass and structure can occur more easily and has unnegligible effects on the dynamic responses of the structure as the mass ratio (M/ml) increases, especially at high velocity of moving mass. Thus, for accurate prediction of the dynamic response of a structure excited by a moving mass, the effect of separation must be taken into account in the analysis.
Localized and Non-Localized Nonlinear Normal Modes in a Multi-Span Beam With Geometric Nonlinearities
Authors: Aubrecht J. , Vakakis A. F.
Published: February 2008

The nonlinear normal modes of a geometrically nonlinear multi-span beam consisting of n segments, coupled by means of torsional stiffeners are examined. Assuming that the stiffeners possess large torsional stiffness, the beam displacements are decomposed into static and flexible components. It is shown that the static components are much smaller in magnitude than the flexible ones. A Galerkin approximation is subsequently employed to discretize the problem, whereby the computation of the nonlinear normal modes of the multi-span beam is reduced to the study of the periodic solutions of a set of weakly coupled, weakly nonlinear ordinary differential equations. Numerous stable and unstable, localized and non-localized nonlinear normal modes of the multi-span beam are detected. Assemblies consisting of n = 2, 3, and 4 beam segments are examined, and are found to possess stable, strongly localized nonlinear normal modes. These are free synchronous oscillations during which only one segment of the assembly vibrates with finite amplitude. As the number of periodic segments increases, the structure of the nonlinear normal modes becomes increasingly more complicated. In the multi-span beams examined, nonlinear mode localization is generated through two distinct mechanisms: through Pitchfork or Saddle-node mode bifurcations, or as the limit of a continuous mode branch when a coupling parameter tends to zero.
An Experimental Study of Structural Health Monitoring Using Incomplete Measurements
Authors: Zimmerman D. C. , Smith S. W. , Kim H. M. , Bartkowicz T. J.
Published: February 2008

In this paper, algorithmic approaches to enhance structural health monitoring capability when faced with incomplete measurements are addressed. The incomplete measurement problem has two aspects: (i) experimental measurement of a lesser number of modes of vibration than that of the analytical model and (ii) experimental measurement of a lesser number of degrees of freedom than that of the analytical model. Studies comparing model reduction, eigenvector expansion, and a hybrid model reduction/eigenvector expansion to address the second contribution are performed using experimental data. These approaches to the incomplete measurement problem are evaluated within the frameworks of multiple-constraint matrix adjustment (both sparsity and nonsparsity preserving algorithms) and minimum rank perturbation theory, which are both applicable for model refinement as well as damage location. Experimental evaluation of the proposed approaches utilize data from the NASA Langley Research Center 8-bay truss and McDonnell Douglas Aerospace 10-bay truss facilities.
Application of the Electromechanical Surface Damping to the Vibration Control of a Cantilever Plate
Authors: Ghoneim H.
Published: February 2008

The electromechanical surface damping technique (EMSD) is applied to suppress the bending and twisting (torsional) peak vibration amplitudes of a cantilever plate. The technique is a combination of the constrained layer damping (CLD) and the shunted piezoelectric methods in which the constraining layer of the CLD is replaced by a shunted piezoelectric ceramic. The frequency responses, to a white noise random base excitation, of the EMSD-treated plate at the vicinity of the first and second bending and twisting resonant frequencies are determined and compared with the corresponding responses of the CLD treatment. It is shown that, in general, the EMSD treatment provides more suppression of the bending and twisting peak vibration amplitudes than the conventional CLD treatment. The EMSD treatment, however, is more effective at higher frequencies and lower temperatures, which suggests that the EMSD method can be applied to extend the effective range of frequencies and/ or temperatures of the conventional CLD method. The work presented is primarily analytical; however, a crude and preliminary experimental work is presented to demonstrate the feasibility of the EMSD technique.
Nonlinear Coupled Vibration Response of Serpentine Belt Drive Systems
Authors: Beikmann R. S. , Perkins N. C. , Ulsoy A. G.
Published: February 2008

This theoretical and experimental study identifies a key nonlinear mechanism that promotes strongly coupled dynamics of serpentine belt drive systems. Attention is focused on a prototypical three-pulley system that contains the essential features of automotive serpentine drives having automatic (spring-loaded) tensioners. A theoretical model is presented that describes pulley and tensioner arm rotations, and longitudinal and transverse belt vibration response. A recent investigation demonstrates that infinitesimal belt stretching creates a linear mechanism that couples transverse belt vibration to tensioner arm rotation. Here, it is further demonstrated that finite belt stretching creates a nonlinear mechanism that may lead to strong coupling between pulley/tensioner arm rotation and transverse belt vibration, in the presence of an internal resonance. Theoretical and experimental results confirm the existence of this nonlinear coupling mechanism. In particular, it is shown that very large transverse belt vibrations can result from small resonant torque pulses applied to the crankshaft or accessory pulleys. These large amplitude transverse vibrations are particularly sensitive to seemingly small changes in the rotational mode characteristics.
Finite Difference Time Marching in the Frequency Domain: A Parabolic Formulation for the Convective Wave Equation
Authors: Baumeister K. J. , Kreider K. L.
Published: February 2008

An explicit finite difference iteration scheme is developed to study harmonic sound propagation in ducts. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.
A Hybrid Inverse Mode Problem for Fixed-Fixed Mass-Spring Models
Authors: Takewaki Izuru , Nakamura Tsuneyoshi , Arita Yasumasa
Published: February 2008

A hybrid inverse mode problem is formulated for a fixed-fixed mass-spring model. A problem of eigenvalue analysis and its inverse problem are combined in this hybrid inverse mode formulation. It is shown if all the masses and the mid-span stiffnesses of the model are prescribed, then the stiffnesses of the left and right spans (side-spans) can be found for a specified lowest eigenvalue and a specified set of lowest-mode drifts in the side-spans. Sufficient conditions are introduced and proved for a specified eigenvalue and a specified set of drifts in the side-spans to provide positive stiffnesses of the side-spans and to be those in the lowest eigenvibration. A set of solution stiffnesses in the side-spans is derived uniquely in closed form.
On-Line Identification of Modal Parameters Using Artificial Neural Networks
Authors: Lim Tae W. , Cabell R. H. , Silcox R. J.
Published: February 2008

Using a neural network concept, an algorithm has been developed that can be employed to conduct on-line identification of modal parameters of a structure such as natural frequency, damping ratio, and mode shape coefficients at measurement locations. Using a band-pass filter, the algorithm extracts from the measurement signal the frequency contents in the vicinity of a desired mode. The filtered signal is then used to train a neural network which consists of a linear neuron with three weights. The structure of the neural network has been designed to allow direct identification of modal parameters from the weights and to enhance efficiency for on-line implementation. The algorithm has been implemented on a DSP (digital signal processor) system for performance evaluation. Modal parameter identification tests have been conducted for a laboratory circular plate structure. The algorithm runs approximately at a sampling frequency of up to 50 kHz for the DSP system used for the study and correctly identifies modal properties of the first two modes of the circular plate. This high performance on-line identification algorithm is expected to be useful in improving the performance of control systems that require knowledge of time-varying plant dynamic characteristics.
Mathematical Analysis of Stability of a Spinning Disk Under Rotating, Arbitrarily Large Damping Forces
Authors: Huang F. Y. , Mote C. D.
Published: February 2008

Stability of a rotating disk under rotating, arbitrarily large damping forces is investigated analytically. Points possibly residing on the stability boundary are located exactly in parameter space based on the criterion that at least one nontrivial periodic solution is necessary at every boundary point. A perturbation technique and the Galerkin method are used to predict whether these points of periodic solution reside on the stability boundary, and to identify the stable region in parameter space. A nontrivial periodic solution is shown to exist only when the damping does not generate forces with respect to that solution. Instability occurs when the wave speed of a mode in the uncoupled disk, when observed on the disk, is exceeded by the rotation speed of the damping force relative to the disk. The instability is independent of the magnitude of the force and the type of positive-definite damping operator in the applied region. For a single dashpot, nontrivial periodic solutions exist at the points where the uncoupled disk has repeated eigenfrequencies on a frame rotating with the dashpot and the dashpot neither damps nor energizes these modes substantially around these points.
Analysis of the Characteristics of Pseudo-Resonance and Anti-Resonance
Authors: Feng-Quan Wang , Xiao-Ling Han , Ying-Zheng Guo
Published: February 2008

In this paper, the analytical expressions of the dynamic compliances of both undamped and damped cantilever beams are found by the transfer funtion method. From these solutions, the phenomenon of “pseudo-resonance” of beams is discovered and defined. The characteristics of resonance and anti-resonance are investigated in detail. The resonance frequencies, anti-resonance frequencies and pseudo-resonance frequencies of the cantilever steel beam are also measured. The calculated results of these resonance characteristics are compared with the experimental ones.
Distributed Piezoelectric Actuators for Shell Interior Noise Control
Authors: Sun J. Q. , Norris M. A. , Rossetti D. J. , Highfill J. H.
Published: February 2008

Structural controls have been recently used to reduce acoustic radiation from vibrating structures. It is well known that in some cases, a control system can reduce the noise and, at the same time, increase the structural vibration. This is one of the concerns with the structural control approach to solve the noise problem. Developing a control system that can reduce the noise and structural vibration at the same time is an important task. This paper proposes one of possible approaches for accomplishing this task. The emphasis of the present approach is not on control strategies, but rather on the design of distributed piezoelectric actuators for the structural control system. In the paper, we study the interior noise radiation and the structural vibrations of uniform cylindrical shells, which are taken as a simplified model of a fuselage section. Two distributed piezoelectric actuators are developed based upon the understanding of the structural-acoustic coupling properties of the system. These actuators can reduce the shell structural vibration and the interior noise at the same time in a wide range of frequencies by using only the acoustic error sensors. Hence, an optimal noise reduction is achieved. Computer simulations and the experiments have shown that the actuators can lead to global noise and vibration reduction. Excellent agreement between the analytical predictions and the experiments strongly supports the theoretical development.
A Residual Flexibility Approach for Decoupled Analysis of Systems of Combined Components
Authors: Spanos P. D. , Majed A.
Published: February 2008

A residual flexibility approach for the analysis of systems involving multiple components subjected to dynamic loading is presented. The reactive forces at the junctions of the components are computed directly without synthesis of component modes or determination of system modes. This is accomplished by expressing the displacements at the junction coordinates of the components in terms of the retained component modes and a first-order account of the residual flexibility of the unretained modes. Once the components are represented in this manner, the requirements of displacement compatibility and force equilibrium at the junction coordinates are enforced. This leads to a set of junction-sized simultaneous algebraic equations for the unknown forces, similar in form to that of the flexibility formulation in statics; this is done by invoking the Newmark integration algorithm. The computed reactive forces at a given time point are used to integrate the equations of motion of the individual components separately for that time point, hence the terminology decoupled analysis. The new method compares well with traditional Component-Mode Synthesis approach for a nonclassically damped fixed-fixed beam consisting of two classically damped cantilevered beam components.
Thermal Storage and Heat Transfer in Phase Change Material Outside a Circular Tube with Axial Variation of the Heat Transfer Fluid Temperature
Authors: Yingqiu Zhu , Yinping Zhang , Yi Jiang , Yanbing Kang
Published: February 2008

A theoretical model is developed to analyze the thermal storage and heat transfer characteristics in a phase change material outside a circular tube with heat transfer fluid inside the tube. A new method, the alternative iteration between temperature and thermal resistance method, is presented to analyze the variation of the phase change radius, the axial temperature variation in the heat transfer fluid and the thermal storage in the circular tube. Dimensionless formulae are developed using theoretical and numerical analysis. The present solutions agree well with those in the literature. The dimensionless correlations are not limited to one condition, so they provide a basis for tube heat transfer design and optimization over a wide range of conditions.
The Maximum Potential Energy Savings from Optimizing Cold Deck and Hot Deck Reset Schedules for Dual Duct VAV Systems
Authors: Liu Mingsheng , Claridge David E.
Published: February 2008

This paper presents the physical models for the maximum potential thermal energy savings from optimizing the hot deck and cold deck reset schedules for dual duct variable air volume systems. The maximum potential savings can be determined by using these models combined with basic system operating parameters and bin data. The system performance can be evaluated by comparing the actual savings with the maximum potential savings. The energy savings from optimal cold deck and hot deck reset schedules in multi-zone buildings should be at least 75 percent of the maximum potential savings.
Free-Vibration of an L-Shaped Plate: The General Solution and an Example of a Simply-Supported Plate With a Clamped Cutout
Authors: Solecki R.
Published: February 2008

This study develops a new accurate method for finding the natural vibration frequencies of plates with cutouts. The method is based on replacing the plate with a cutout by a rectangular plate. This is achieved by filling the cutout with a “dummy” plate made of the same material, and of the same thickness as the original from which it is separated by an infinitesimal gap. Thanks to this device it is possible to apply finite Fourier transformation of discontinuous functions in a rectangular domain. The expression for the deflection now depends on the unknown quantities along the boundary and across the gap. Subsequent application of the available boundary conditions leads to a system of boundary integral equations. An L-shaped plate simply supported along the perimeter, and fixed along the cutout, is analyzed as an example. The frequencies of natural vibration are calculated and compared with the results obtained using the finite element method. The method presented here is also applicable to two- and three-dimensional problems of solids with holes or cavities and to similar thermoelastic problems. Application to plates with curved boundaries is also possible.
The Use of Optimally Shaped Piezo-electric Film Sensors in the Active Control of Free Field Structural Radiation, Part 2: Feedback Control
Authors: Snyder S. D. , Tanaka N. , Kikushima Y.
Published: February 2008

Feedback control of free field structural radiation is considered. State equations are formulated with a transformation which decouples the acoustic power error criterion. Using the resultant equations, expressed in terms of “transformed mode” states, the order of the state equations can be significantly reduced at low frequencies. Two experimental implementations of feedback control strategies using shaped piezoelectric polymer film sensors to measure the transformed system states are described. The first of these is a simple analog implementation. The second implementation is in discrete time, where an adaptive algorithm for optimizing the weights of IIR filters for practical use is described. It is shown that by using the outlined control approach significant levels of low frequency acoustic power attenuation can be obtained with no control spillover and subsequent increase in higher frequency acoustic power output.
Piezoelectric Modal Sensor/Actuator Design for Monitoring/Generating Flexural and Torsional Vibrations of Cylindrical Shells
Authors: Sung C. K. , Chen T. F. , Chen S. G.
Published: February 2008

This paper presents a methodology for designing piezoelectric sensors/actuators in an application to monitor/generate flexural and torsional vibrations of cylindrical shells. Based upon the classical laminate theory the equations of the electro-mechanical interactions, the constitutive, and the strain-displacement relations of piezoelectric composite cylindrical shells are derived. With these relations the piezoelectric sensor and actuator equations of the cylindrical shell are then developed. The modal sensors/actuators fabricated with PVDF embedded in the composite cylindrical shell capable of monitoring and generating vibrations of a particular mode or several combined modes are also developed. Finally, an experimental rig is designed to generate both the flexural and torsional vibrations of a circular cylindrical shaft for examining the capabilities of the modal sensors.
Robustness of Natural Controls of Distributed-Parameter Systems
Authors: Hwang Jai Hyuk , Kim Doo Man , Lim Kyoung Ho
Published: February 2008

In this paper, the effect of parameter and spatial discretization errors on the closed-loop behavior of distributed-parameter systems is analyzed for natural controls. If the control force designed on the basis of the postulated system with the parameter and discretization errors is applied to control the actual system, the closed-loop performance of the actual system will be degraded depending on the degree of the errors. The extent of deviation of the closed-loop performance from the expected one is derived and evaluated using operator techniques. It has been found that the extent of the deviation is proportional to the magnitude of the parameter and discretization errors, and that the proportional coeffecient depends on the structures of the natural controls.
Application of the Taylor Transform to Nonlinear Vibration Problems
Authors: Chiou J. S. , Tzeng J. R.
Published: February 2008

A new transformation technique called the Taylor transform is introduced in this study. A great advantage of the Taylor transform over the integral transform is its ability to solve the nonlinear differential equation. Two nonlinear problems—Van der Pol’s equation and the motion behavior of an earthquake isolation system—are solved by the present method. The results compare very well with the measured data and the results obtained from other analytical methods.
Long Term Structural Dynamics of Mechanical Systems With Local Nonlinearities
Authors: Fey R. H. B. , van Campen D. H. , de Kraker A.
Published: February 2008

This paper deals with the long term behavior of periodically excited mechanical systems consisting of linear components and local nonlinearities. The number of degrees of freedom of the linear components is reduced by applying a component mode synthesis technique. Lyapunov exponents are used to identify the character of the long term behavior of a nonlinear dynamic system, which may be periodic, quasi-periodic or chaotic. Periodic solutions are calculated efficiently by solving a two-point boundary value problem using finite differences. Floquet multipliers are calculated to determine the local stability of these solutions and to identify local bifurcation points. The methods presented are applied to a beam system supported by a one-sided linear spring, which reveals very rich, complex dynamic behavior.
Effect of Axial Load on Free Vibration of Orthotropic Truncated Conical Shells
Authors: Tong L.
Published: February 2008

An analytical solution in the form of a power series is obtained for the three governing equations of free vibrations of axially loaded orthotropic conical shells. Numerical results are presented for the frequency parameters and the associated circumferential wave numbers of the axially loaded shells with different geometric and material parameters and under two types of boundary conditions. It is noted that the axially compressive load decreases the frequency parameters while the axial tension load increases the frequency parameters.
Three-Dimensional Analysis of the Free Vibration of Thick Rectangular Plates With Depressions, Grooves or Cut-Outs
Authors: Young P. G. , Yuan J. , Dickinson S. M.
Published: February 2008

A solution is presented for the free vibration of very thick rectangular plates with depressions, grooves or cut-outs using three-dimensional elasticity equations in Cartesian coordinates. Simple algebraic polynomials which satisfy the boundary conditions of the plate are used as trial functions in a Ritz approach. The plate is modelled as a parallelepiped, and the inclusions are treated quite straightforwardly by subtracting the contribution to the strain and kinetic energy expressions of the volume removed, before minimizing the functional. The approach is demonstrated by considering a number of square thick plate cases, including a plate with a cylindrical groove, a shallow depression or a cylindrical cut-out.
Operation of a Four-Bar Mechanism Above Several Critical Speeds
Authors: Aannaque A. , Garvey S. , Bennouna M. , Penny J.
Published: February 2008

A dynamic analysis of a four-bar mechanism shows that it has many critical speeds where the response of the system is large compared to the response at neighboring speeds. Some of these critical speeds are limiting critical speeds. The lowest of these limiting speeds cannot be exceeded because stresses in one of the links would become greater than the safe working stress. This paper examines methods for computing critical speeds and suggests a method whereby the first limiting critical speed of a mechanism can be adjusted either continuously or discretely so that speeds above the first limiting critical speed can be achieved without the mechanism ever experiencing undue duress.
Disk/Shaft Vibration Induced by Bearing Clearance Effects: Analysis and Experiment
Authors: Flowers G. T. , Wu Fangsheng
Published: February 2008

This study presents an investigation of the dynamics of a rotor system with bearing clearance. Of particular interest is the influence of such effects on coupled disk/shaft vibration. Experimental results for a rotor system with a flexible disk are presented and compared to predictions from a simulation model. Some insights and conclusions are obtained with regard to the conditions under which such vibration may be significant.
Liapunov-Floquet Transformation: Computation and Applications to Periodic Systems
Authors: Sinha S. C. , Pandiyan R. , Bibb J. S.
Published: February 2008

In this paper, a new analysis technique in the study of dynamical systems with periodically varying parameters is presented. The method is based on the fact that all linear periodic systems can be replaced by similar linear time-invariant systems through a suitable periodic transformation known as the Liapunov-Floquet (L-F) transformation. A general technique for the computation of the L-F transformation matrices is suggested. In this procedure, the state vector and the periodic matrix of the linear system equations are expanded in terms of the shifted Chebyshev polynomials over the principal period. Such an expansion reduces the original differential problem to a set of linear algebraic equations from which the state transition matrix (STM) can be constructed over the period in closed form. Application of Floquet theory and eigenanalysis to the resulting STM yields the L-F transformation matrix in a form suitable for algebraic manipulations. The utility of the L-F transformation in obtaining solutions of both linear and nonlinear dynamical systems with periodic coefficients is demonstrated. It is shown that the application of L-F transformation to free and harmonically forced linear periodic systems directly provides the conditions for internal and combination resonances and external resonances, respectively. The application of L-F transformation to quasilinear periodic systems provides a dynamically similar quasilinear systems whose linear parts are time-invariant and the solutions of such systems can be obtained through an application of the time dependent normal form theory. These solutions can be transformed back to the original coordinates using the inverse L-F transformation. Two dynamical systems, namely, a commutative system and a Mathieu type equation are considered to demonstrate the effectiveness of the method. It is shown that the present technique is virtually free from the small parameter restriction unlike averaging and perturbation procedures and can be used even for those systems for which the generating solutions do not exist in the classical sense. The results obtained from the proposed technique are compared with those obtained via the perturbation method and numerical solutions computed using a Runge-Kutta type algorithm.
Vibration of a Spinning Cylindrical Shell With Internal/External Ring Stiffeners
Authors: Huang Shyh-Chin , Chen Lin-Hung
Published: February 2008

The paper presents an approach to the vibration analysis of a spinning cylindrical shell with internal, symmetric, or external ring stiffeners. A modified receptance method for spinning structures is employed in this analysis. Various numerical examples are demonstrated and the results are compared with the existing data. The effects of types, numbers of stiffeners and of spin speed on the shell frequencies are extensively discussed. The results show that for no spin the ring stiffeners stiffen only then > 1 modes (n–circumferential wave number), and the stiffening effect become more significant with the increasing n number. With spin, the rings stiffen the forward modes in a way similar to the non-spin cases. The backward modes are however all stiffened by the attached rings for all n values. Among the three types of rings, on backward modes, the internal rings always have a better stiffening effect, then the symmetric and the external rings. As to the forward modes, as spinning speed increases, the external rings raise the shell’s frequencies faster than the others due to the largest centrifugal force. At last, the effects of the ring’s location, stiffness, and mass density on the frequency changes are examined. Numerical results show that the sensitivity of the shell’s frequencies to these parameters increases with the spin speed. Among the shell modes, the lower n modes are affected more by these parameters.
Multibody Dynamics Incorporating Deployment of Flexible Structures
Authors: Tadikonda S. S. K. , Singh R. P. , Stornelli S.
Published: February 2008

The equations of motion for a flexible structure during deployment from and retraction into a base that is part of an open-loop multi-body chain are derived. The eigenfunctions of a fixed-free beam are used as the shape functions and their properties are exploited to express various domain integral terms as explicit functions of the instantaneous deployed length. The essential contributions of the present paper are the modeling of flexible body deployment with mass transfer and a recursive solution method for the dynamics. The deployment or retraction of space structures such as the SAFE Extension Mast can be simulated using this model. The model is presented in a format that is suitable for implementation in multibody dynamics codes.
Active Vibration Absorption Using Delayed Resonator With Relative Position Measurement
Authors: Olgac N. , Hosek M.
Published: February 2008

A novel active vibration absorption technique, the Delayed Resonator, has been introduced recently as a unique way of suppressing undesired oscillations. It suggests a control force on a mass-spring-damper absorber in the form of a proportional position feedback with a time delay. Its strengths consist of extremely simple implementation of the control algorithm, total vibration suppression of the primary structure against a harmonic force excitation and full effectiveness of the absorber in a semi-infinite range of disturbance frequency, achieved by real-time tuning. All this development work was done using the absolute displacements of the absorber in the feedback. These measurements, however, may be difficult to obtain and for some applications impossible. This paper deals with the operating and design repercussions caused by the substituting of an easier measurement: the relative motion of the absorber with respect to the primary structure. Although the proposition sounds like a trivial extension to the prior work it gives rise to important concerns such as system stability. Theoretical foundations for the Delayed Resonator (DR) are briefly recapitulated and its implementation on a single-degree-of-freedom primary structure disturbed by a harmonic force is discussed utilizing both absolute and relative position measurement of absorber mass. Methods for stability range analysis and transient behavior are presented as design tools. Properties observed for the same system with these two different feedbacks are compared. Another important advantage of the relative position feature is is to decouple the operation of the absorber from the primary structure entirely.
Dynamic Behavior of a Harmonically Excited Electromechanical Drive With Elastic Couplings
Authors: Chaika V. , Mariunas M.
Published: February 2008

Steady-state vibration of a lumped rotary system containing an electric drive is considered. The system is subjected to the harmonic excitation caused by the variation of voltage of the electric motor and the resisting torque of the operating machine. The influence of several types of elastic couplings on the dynamic behavior of an electromechanical drive is investigated. Numerical-analytical methods of nonlinear vibration analysis are applied. Frequency-response curves of rotary machines for different coupling cases are obtained. A numerical optimization technique for the estimation of the rational parameter values of the system is developed. Vibration controlling properties of standard and centrifugal couplings are compared.
Modeling, Actuation, and Control of an Active Fluid Vibration Isolator
Authors: Panza M. J. , McGuire D. P. , Jones P. J.
Published: February 2008

An integrated mathematical model for the dynamics, actuation, and control of an active fluid/elastomeric tuned vibration isolator in a two mass system is presented. The derivation is based on the application of physical principles for mechanics, fluid continuity, and electromagnetic circuits. Improvement of the passive isolator performance is obtained with a feedback scheme consisting of a frequency shaped notch compensator in series with integral control of output acceleration and combined with proportional control of the fluid pressure in the isolator. The control is applied via an electromagnetic actuator for excitation of the fluid in the track connecting the two pressure chambers of the isolator. Closed loop system equations are transformed to a nondimensional state space representation and a key dimensionless parameter for isolator-actuator interaction is defined. A numerical example is presented to show the effect of actuator parameter selection on system damping, the performance improvement of the active over the passive isolator, the robustness of the control scheme to parameter variation, and the electrical power requirements for the actuator.
Active and Reactive Structural Energy Flow
Authors: Alfredsson K. S.
Published: February 2008

Vibration of linear structures having internal material damping is considered. Energy supplied to such structures by external dynamic loads and mechanical energy flow inside these structures are investigated. The paper aims at presenting and discussing relations which are useful when studying energy transmission through mechanical systems. Special attention is paid to the case of stationary harmonic vibration, but general stationary vibration is also discussed. Continuity equations for the active and reactive mechanical intensities are derived for a solid continuum model. Limits for the active and reactive power supplied to a structure in terms of structural and loading properties are also established. Numerical examples with discrete, continuous and discretized structures demonstrate the results obtained.
Natural Frequencies and Stability of an Axially-Traveling String in Contact With a Stationary Load System
Authors: Chen Jen-San
Published: February 2008

The natural frequencies and stability of a string traveling between two fixed supports and in contact with a stationary load system, which contains such parameters as dry friction, inertia, damping, and stiffness, are investigated both numerically and analytically. After establishing the orthogonality properties between the eigenfunctions of a freely traveling string, the eigenvalues of the coupled system are calculated by a numerical procedure based on eigenfunction expansion method. It is found that the stiffness in the load system tends to increase the natural frequencies of the traveling string, while the inertia tends to decrease the natural frequencies. When the load system contains both inertia and stiffness elements with natural frequency ωz, inertia effect is dominant for the modes with natural frequencies higher than ωz, and stiffness effect is dominant for the modes with natural frequencies lower than ωz. Large dry friction causes flutter instability in the high speed range, which cannot be suppressed by the damping element in the load system. The expressions for the derivatives of eigenvalues with respect to various load parameters are derived to verify the numerical results.
Design Sensitivity Analysis of Structure-Induced Noise and Vibration
Authors: Choi K. K. , Shim I. , Wang S.
Published: February 2008

A continuum design sensitivity analysis (DSA) method for dynamic frequency responses of structural-acoustic systems is developed using the adjoint variable and direct differentiation methods. A variational approach with a non-self-adjoint operator for complex variables is used to retain the continuum elasticity formulation throughout derivation of design sensitivity results. It is shown that the adjoint variable method is applicable to the variational equation with the non-self-adjoint operator. Sizing design variables such as the thickness and cross-sectional area of structural components are considered for the design sensitivity analysis. A numerical implementation method of continuum DSA results is developed by postprocessing analysis results from established finite element analysis (FEA) codes to obtain the design sensitivity of noise and vibration performance measures of the structural-acoustic systems. The numerical DSA method presented in this paper is limited to FEA and boundary element analysis (BEA) is not considered. A numerical method is developed to compute design sensitivity of direct and modal frequency FEA results. For the modal frequency FEA method, the numerical DSA method provides design sensitivity very efficiently without requiring design sensitivities of eigenvectors. The numerical method has been tested using passenger vehicle problems. Accurate design sensitivity results are obtained for analysis results obtained from established FEA codes.
Design of Experiments for the Controller of Rotor Systems With a Magnetic Bearing
Authors: Sheu G. J. , Yang S. M. , Yang C. D.
Published: February 2008

A new design methodology for the vibration control of rotor systems with a magnetic bearing is developed in this paper. The methodology combines the experimental design method in quality control engineering and the conventional PD control technique such that their advantages in implementation feasibility and performance-robustness can be integrated together. A quality loss index defined by the summation of the infinity norm of unbalanced vibration is used to characterize the system dynamics. By using the location of the magnetic bearing and PD feedback gains as design parameters, the controller can be determined by a small number of matrix experiments to achieve the best system performance. In addition, it is robust to the vibration modes within a desired speed range. A rotor system consisting of 4 rigid disks, 3 isotropic bearings, and 1 magnetic bearing is applied to illustrate the feasibility and effectiveness of the experiment-aided controller design.
A Driver’s Seat With Active Suspension of Electro-pneumatic Type
Authors: Stein G. J.
Published: February 2008

The aim of this article is to summarize some of the results of a study of a driver’s seat with an electro-pneumatic active suspension utilizing a pneumatic spring and a proportional electro-pneumatic transducer. Discussion of the system’s simplified mathematical description is followed by a short explanation of the full scale dummy driver’s seat with active pneumatic suspension and discussion of some experimental results.
Stick-Slip Motion of Frictionally Damped Turbine Airfoils: A Finite Element in Time (FET) Approach
Authors: Wang Yu
Published: February 2008

A method is proposed for analyzing the periodic stick-slip motion of a single degree of freedom model of frictionally damped turbine blades. The method of finite elements in the time domain (FET) is based on a Hamilton’s weak principle, paralleling the variational methods in elastostatics. It permits a complete determination of the hysteretic friction force, and results in a set of highly structured system equations. The method has a number of unique features, which are utilized to provide a simple yet efficient approach for predicting the steady-state response. When applied to a number of example problems, including systems with static friction and the excitation of multiple discrete frequencies, the FET method is demonstrated to be an efficient and reliable alternative technique for nonlinear dynamic response analysis.
The Effect of Thermal Prestress on the Free Vibration Characteristics of Clamped Rectangular Plates: Theory and Experiment
Authors: Murphy K. D. , Virgin L. N. , Rizzi S. A.
Published: February 2008

In a combined theoretical and experimental approach, the free vibration characteristics of a uniformly heated, fully clamped (out-of-plane), rectangular plate are considered. Specifically, this work focuses on the behavior of the small amplitude natural frequencies as the temperature is increased from the ambient. The effects of initial geometric imperfections, modal coupling, imperfect clamping (in-plane) and post-buckling are addressed. Comparisons between theory and experiment show excellent agreement.