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TECHNICAL PAPERS

J. Vib. Acoust. 2002;124(3):329-333. doi:10.1115/1.1471528.

A classical way of improving acoustical absorption performances of porous materials is the use of corrugated surfaces; this use can obtain lower cut-off frequencies and also improve the overall absorption over a wide frequency range. An analytical approximation is presented for the calculus of the absorption on this kind of surfaces, where the thickness gradient is represented as a series of steps. Reflection coefficient of every step is obtained and will contribute to the net reflection coefficient. Theoretical results will be presented and shown to agree with experimental data.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2002;124(3):334-339. doi:10.1115/1.1471358.

This paper investigates the acoustic and flow performance of an intake system using numerical and experimental techniques. The acoustic and flow performances are characterized by computing the Insertion Loss (IL) and the loss coefficient (LC) respectively. An indirect BEM formulation is used to predict the IL. The LC is computed by solving a one-dimensional fluid dynamics problem. For four simple cylindrical duct systems, numerical results for IL and LC are compared with experimental measurements. Finally, the acoustic and flow performance of an actual motorcycle intake is predicted and the results are compared to bench test results.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2002;124(3):340-349. doi:10.1115/1.1467649.

A complex variable description of planar motion incorporates directivity as inherent information which is therefore very convenient in vibration analysis of rotors. This paper proposes to use the directional information explicitly when the equation of motion of a rotor is formulated in complex variables. It is shown that the free vibration solution to the equation of motion formulated as such can be defined as the directional natural mode because it describes not only the shape and frequency but also the direction of the free vibration response. The directional frequency response functions (dFRFs) that have been used recently are obtained as the solution to the forced vibration solution to the equation of motion. Symmetric and anti-symmetric motions of a geometrically symmetric rigid rotor are used as examples to explain these concepts and their practical significances. The proposed approach allows clear understanding and definitions of some unique characteristics of rotor vibrations, such as the forward and backward modes, and forward and backward critical speeds, which have been often used in confusing or incorrect ways.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2002;124(3):350-358. doi:10.1115/1.1467648.

There are a variety of abnormal running conditions in rotating machinery that lead to rotor/stator interaction dynamics which, in turn, have a range of effects associated with them. One of these effects is steady vibration response at frequencies which are different from the excitation. This paper describes a mechanism of generating subharmonic vibration frequencies in both numerical simulation and measurements, which are obtained from a study of the relatively new problem of “windmilling imbalance” in aero-engines. What is different from other nonlinear systems with, say, clearance or squeeze film dampers, is the richness of the frequency spectrum.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2002;124(3):359-366. doi:10.1115/1.1467652.

This paper provides a new algorithm and test verification for implementing fault-tolerant operation of magnetically suspended, flexible shaft, rotating machinery. The currents to the magnetic bearing are redistributed in a manner so that the bearing actuator preserves the same linearized magnetic forces after some of its coils experience failure. The algorithm that searches a database for the appropriate failure compensation matrix utilizes a Boolean description of the failure state to quickly locate and download its target. The test results are shown to have good agreement with the system simulation results presented.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2002;124(3):367-375. doi:10.1115/1.1473831.

Massless bilinear hysteresis elements are often used to model frictional energy dissipation in dynamic systems. These quasi-static elements possess only two describing parameters, the damper stiffness and the force at which it slips. Bilinear hysteresis elements capture the qualitative nature of friction-damped forced response, but sometimes have difficulty with quantitative comparisons. This paper examines the performance of massless bilinear hysteresis elements as well as the role of damper mass in energy dissipation, and specifically evaluates its influence on the kinematic state of the damper (pure slip, stick-slip, pure stick). Differences between the massless and non-zero mass case are explored, as are the implications on both damper and system response. The results indicate that even small damper mass can have a qualitative effect on the system response, and provide advantages over the massless case. Further, we develop transition maps, describing damper response kinematics in the damper parameter space, which segment the space into two linear analysis regions (pure slip, pure stick) and one nonlinear analysis region (stick-slip). The results suggest non-zero mass dampers which are tuned as optimal vibration absorbers provide substantial resonance response attenuation and substantially reduce the size of the nonlinear analysis region in the damper parameter space.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2002;124(3):376-386. doi:10.1115/1.1469007.

We present a spectral finite element model (SFEM) for sandwich beams with passive constrained layer damping (PCLD) treatments. The viscoelastic core has a complex modulus that varies with frequency. The SFEM is formulated in the frequency domain using dynamic shape functions based on the exact displacement solutions from progressive wave methods, where we implicitly account for the frequency dependent complex modulus of the viscoelastic core. The SFEM results of natural frequencies and frequency response functions are compared to those calculated using conventional finite element (CFEM), where the Golla-Hughes-McTavish method is used to account for the frequency dependent complex modulus of a viscoelastic core. Also experimental data are used to validate both analyses using frequency response functions measured for two cantilevered sandwich beams with PCLD treatments having 50% and 75% coverage of the beam length. SFEM shows improved computational efficiency and accuracy, because many more elements must be incorporated into the CFEM for comparable accuracy.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2002;124(3):387-396. doi:10.1115/1.1467650.

Free vibration analysis of a free inflated torus of circular cross-section is presented. The shell theory of Sanders, including the effect of pressure, is used in formulating the governing equations. These partial differential equations are reduced to ordinary differential equations with variable coefficients using complete waves in the form of trigonometric functions in the longitudinal direction. The assumed mode shapes are divided into symmetric and antisymmetric groups, each given by a Fourier series in the meridional coordinate. The solutions (natural frequencies and mode shapes) are obtained using Galerkin’s method and verified with published results. The natural frequencies are also obtained for a circular cylinder with shear diaphragm boundary condition as a special case of the toroidal shell. Finally, the effects of aspect ratio, pressure, and thickness on the natural frequencies of the inflated torus are studied.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2002;124(3):397-409. doi:10.1115/1.1468870.

In this study, the dynamic stiffness method is employed for the free vibration analysis of helical springs. This work gives the exact solutions for the natural frequencies of helical beams having arbitrary shapes, such as conical, hyperboloidal, and barrel. Both the cross-section dimensions and the shape of the beam can vary along the axis of the curved member as polynomial expressions. The problem is described by six differential equations. These are second order equations with variable coefficients, with six unknown displacements, three translations, and three rotations at every point along the member. The proposed solution is based on a new finite-element method for deriving the exact dynamic stiffness matrix for the member, including the effects of the axial and the shear deformations and the rotational inertia effects for any desired precision. The natural frequencies are found as the frequencies that cause the determinant of the dynamic stiffness matrix to become zero. Then the mode shape for every natural frequency is found. Examples are given for beams and helical springs with different shape, which can vary along the axis of the member. It is shown that the present numerical results agree well with previously published numerical and experimental results.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2002;124(3):410-413. doi:10.1115/1.1473829.

A finite element/boundary element design tool is used to perform a structural acoustic optimization on an eight-ply graphite epoxy cylindrical shell. The shell is subject to two external monopole sources vibrating at a single frequency. The goal of the optimization is the minimization of the sum of the squared pressure amplitudes within the enclosed acoustic cavity. The ply angles serve as the design variables in optimization. The optimal design was obtained after 15 iterations with a 2 dB reduction in the average interior sound pressure level. The ply angle orientation shifted from an initially symmetric lay-up to an unsymmetric lay-up in the final design.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2002;124(3):414-419. doi:10.1115/1.1467653.

This paper is aimed at identifying a dynamical model for an acoustic enclosure, a duct with rectangular cross section, closed ends, and side-mounted speaker enclosures. Acoustic enclosures are known to be resonant systems of high order. In order to design a high performance feedback controller for an acoustic enclosure, one needs to have an accurate model of the system. Subspace-based system identification techniques have proven to be an efficient means of identifying dynamics of high order highly resonant systems. In this paper a frequency domain subspace-based method together with a second iterative optimization step minimizing a frequency domain least-squares criterion is successfully employed to identify a dynamical model for an acoustic enclosure.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2002;124(3):420-426. doi:10.1115/1.1468869.

Stability and bifurcation for the unsymmetrical, periodic motion of a horizontal impact oscillator under a periodic excitation are investigated through four mappings based on two switch-planes relative to discontinuities. Period-doubling bifurcation for unsymmetrical period-1 motions instead of symmetrical period-1 motion is observed. A numerical investigation for symmetrical, period-1 motion to chaos is completed. The numerical and analytical results of periodic motions are in very good agreement. The methodology presented in this paper is applicable to other discontinuous dynamic systems. This investigation also provides a better understanding of such an unsymmetrical motion in symmetrical discontinuous systems.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2002;124(3):427-434. doi:10.1115/1.1473828.

A general methodology is presented for investigating ride dynamics of large order vehicle models in a systematic and computationally efficient way. First, the equations of motion of representative vehicle models are set up by applying classical finite element techniques. In the simplest version of these models, the important system parameters are assumed to be constant, leading to linear formulations. Then, more accurate and involved models are examined by including typical nonlinearities in the tires and the shock absorbers of the vehicle suspension. Also, emphasis is placed on taking into account the possibility of temporary separation of a wheel from the ground. These models are strongly nonlinear and as their order increases the existing numerical methodologies for a systematic determination of their dynamics become inefficient to apply. Therefore, the first step of the present methodology is to reduce the dimensions of the original system by applying a component mode synthesis approach. Subsequently, this allows the application of appropriate numerical methodologies for predicting response spectra of the nonlinear models to periodic road excitations. Finally, results obtained by direct integration of the equations of motion are also presented for transient road excitation. In all cases, the accuracy and validity of the applied methodology is verified by comparison with results obtained for the original models.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2002;124(3):435-440. doi:10.1115/1.1476381.

This paper proposes an adaptive boundary control to an axially moving string system, which couples with a mass-damper-spring (MDS) controller at its right-hand-side (RHS) boundary. Unknown parameters appearing in the system equation are assumed constant and estimated on-line by using adaptation laws. The adaptive computed-torque control algorithm applied to robot manipulators of lumped systems is extended to design the adaptive boundary controller for the coupling system. It is found that the control force and update laws depend only on the displacement, velocity and slope of the string at the RHS boundary. Lyapunov stability guarantees the convergence of the tracking error to zero. Finally, the performance of the proposed controller is demonstrated by numerical simulations.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2002;124(3):441-450. doi:10.1115/1.1473830.

This paper presents the development, design, and implementation of a precision control system for a large, sparse-aperture space-deployable telescope testbed. Aspects of the testbed and laboratory environment relevant to nanometer-level control and performance objectives are provided. There are four main objectives of the control system: 1) reduction of natural resonances of the supporting structure, 2) rejection of tonal disturbances, 3) tip, tilt, and piston set-point tracking for optical surfaces, and 4) reduction in settling time of optical surfaces after an impulsive slew-type disturbance. The development of a three-input, three-output, high-bandwidth structural control system for the testbed is presented, and experimental data demonstrating that all objectives were attained is provided. The paper concludes with a discussion of the results and a description of research issues remaining to be addressed.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J. Vib. Acoust. 2002;124(3):451-454. doi:10.1115/1.1467651.

A simple design formula is derived here to evaluate the fundamental frequency parameter of initially stressed (subjected to axial concentrated load at the ends) uniform beams resting on elastic foundation. Even though the basis for derivation of the formula is based on the finite element method, the applicability of the formula is general and can be used effectively, once the buckling load parameter, stress free frequency parameter and the applied concentrated load parameter are known, to obtain the fundamental frequency parameter of the stressed beam. The assumption involved in deriving the formula is that the mode shapes of buckling, stress free vibration and stressed vibration are the same. The effectiveness of the formula is demonstrated through numerical examples.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2002;124(3):454-460. doi:10.1115/1.1471357.

This paper presents an analytical technique for the analysis of a stochastic dynamic system whose damping behavior is described by a fractional derivative of order 1/2. In this approach, an eigenvector expansion method is used to obtain the response of the system. The properties of Laplace transforms of convolution integrals are used to write a set of general Duhamel integral type expressions for the response of the system. The general response contains two parts, namely zero state and zero input. For a stochastic analysis, the input force is treated as a random process with specified mean and correlation functions. An expectation operator is applied on a set of expressions to obtain the stochastic characteristics, namely the variance and covariance responses of the system. Closed form stochastic response expressions are obtained for white noise. Numerical results are presented to show the stochastic response of a fractionally damped system subjected to white noise. Results show that stochastic response of the fractionally damped system oscillates even when the damping ratio is greater than its critical value.

J. Vib. Acoust. 2002;124(3):460-464. doi:10.1115/1.1476382.

This paper studies numerically the motion of an AMB rotor when it is supported only by backup bearings. Unlike a linear rotor-bearing system, which always undergoes a harmonic motion, the nonlinear AMB rotor-backup bearing system will undergo irregular or chaotic motion at some rotating speeds. The simulations show that in a wide rotating speed range there are several extra resonance frequencies, which are different from those appearing in well-known linear models. When a power failure occurs to AMB machinery, the AMB rotor should pass through all these resonance frequencies. Under some conditions, the full clearance whirl motion of the rotor in backup bearings will happen, which may lead to damage. In this paper several measures that could reduce the nonlinear response and hence avoid the full clearance motion are discussed.

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