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IN THIS ISSUE

### TECHNICAL PAPERS

J. Vib. Acoust. 2006;129(2):133-140. doi:10.1115/1.2424975.

This paper discusses the effects of compression on acoustical performance of fibrous materials. A finite element model is used to predict the absorption coefficient and transmission loss of absorbing and barrier materials. This model is developed based on the Galerkin method and includes the equation of wave propagation in rigid frame porous material. The compression of fibrous material is entered to the model with relations that explain modifications of physical properties used in the wave equation. Acoustical behavior of absorption and barrier materials with and without compression is studied. It is shown that compression of the material leads to reduction of the transmission loss of the barrier materials and absorption coefficient of absorbing materials. In this regard, “thickness reduction” and “variations of physical parameters” due to compression are investigated.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2006;129(2):141-147. doi:10.1115/1.2202357.

The mode interactions and the sound transmission loss across the expansion chambers with and without tapered sections are studied by the finite element method in the present investigation. Results from chambers with symmetrical inlet and outlet suggest lower sound power transmission loss at frequencies below that of the first symmetrical transverse chamber mode when the tapered section angle is reduced. Weak sound power transmission loss is also observed for this chamber type at frequency higher than that of the first symmetrical duct mode. Numerous high and low sound power transmission loss regions are observed between these two eigenfrequencies. Higher plane wave power transmission loss can be found at smaller tapered section angle only if one of the chamber endings is not tapered. Such chamber bears important industrial application.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2006;129(2):148-157. doi:10.1115/1.2202152.

This paper presents the modeling, testing, and validation methodologies developed to predict the optical performance of the Space Interferometry Mission (SIM) at the Jet Propulsion Laboratory (JPL). The modeling methodology combines structural, optical, and control system design within a common state space framework and incorporates reaction wheel assembly (RWA) disturbances to evaluate the end-to-end performance of the system requirements. The validation methodology uses the Micro-Precision Interferometer (MPI) testbed, which is a ground-based, representative hardware model of SIM. In this study, the integrated model of the MPI testbed was used to calculate the transfer functions from RWA input to optical performance output. The model-predicted transfer functions were compared with the MPI testbed measurements, and the accuracy of the integrated model was quantified using a metric that was based on output power of the transfer functions. The RWA disturbances were then propagated through the modeled and measured transfer functions to predict the optical performance of the MPI testbed. This method is called the “decoupled disturbance analysis” and relies on the “blocked” RWA disturbances, measured with the RWA hardmounted to a rigid surface. These predictions were compared with the actual (measured) optical performance of MPI, measured with the RWA mounted to MPI, to evaluate the accuracy of the decoupled disturbance analysis method. The results show that this method is not an accurate representation of the coupled boundary conditions that occurs when the RWA is mounted to the flexible MPI structure. In order to correct for the blocked RWA disturbance boundary conditions, the “coupled disturbance analysis” method was developed. This method uses “force filters” that depend on estimates of the interface accelerances of the RWA and the MPI structure to effectively transform the blocked RWA disturbance measurements into their corresponding “coupled” disturbances (the disturbances that would occur at the coupled RWA-MPI interface). Compared to the decoupled method, the coupled method more accurately predicts the system’s performance. Additionally, the RWA cross-spectral density terms were found to be influential in matching the performance predictions to the measured optical performance of MPI.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2006;129(2):158-168. doi:10.1115/1.2424984.

Viscoelastic materials are often used to add damping to metal structures, usually via the constrained layer damping method. The added damping depends strongly on material temperature and frequency, as do the underlying material properties of the viscoelastomer. Several standardized test methods are available to characterize the dynamic material properties of viscoelastomers. However, they rely on limited test data which is extrapolated using the time—temperature superposition technique. The authors have found that the different testing methods typically produce significantly different dynamic material properties, or “master curves.” An approach for inferring viscoelastomer dynamic moduli with better accuracy is suggested here. Several metal bars are treated using constrained layer damping. Experimental modal analyses are conducted on the bars at different temperatures to produce sets of system resonance frequencies and loss factors. Corresponding finite element (FE) models of the treated bars are analyzed using assumed viscoelastomer material properties based on master curves generated using a standardized test technique. The parameters which define the master curves are adjusted by trial and error until the FE-simulated system loss factors match those of the measurements. The procedure is demonstrated on two viscoelastomers with soft and stiff moduli.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2006;129(2):169-178. doi:10.1115/1.2424969.

This paper presents a fast adaptive time–frequency analysis method for dealing with the signals consisting of stationary components and transients, which are encountered very often in practice. It is developed based on the short-time Fourier transform but the window bandwidth varies along frequency adaptively. The method therefore behaves more like an adaptive continuous wavelet transform. We use B-splines as the window functions, which have near optimal time–frequency localization, and derive a fast algorithm for adaptive time–frequency representation. The method is applied to the analysis of vibration signals collected from rotating machines with incipient localized defects. The results show that it performs obviously better than the short-time Fourier transform, continuous wavelet transform, and several other most studied time–frequency analysis techniques for the given task.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2006;129(2):179-192. doi:10.1115/1.2424970.

Active vibration isolation from an arbitrarily, structurally complex receiver is considered with respect to the impacts of structure flexibility on the open- and closed-loop system characteristics. Specifically, the generally weak influence of flexibility on the open-loop transfer function in the case of total force feedback, in contrast to acceleration feedback, is investigated. The open-loop system characteristics are analyzed based on open-loop transfer function expressions obtained using modal expansion and on modal model order reduction techniques. To closely demonstrate and illustrate the impacts of flexibility on the closed-loop system performance and stability, a problem of automotive engine vibration isolation from a flexible subframe is presented where the neglected dynamics are represented as an output multiplicative model perturbation. A physical explanation as to why the contribution of flexibility to the open-loop transfer function could be neglected in the case of total force feedback in contrast to acceleration feedback is given. Factors for an individual eigenmode to not significantly contribute to the total force output are presented where the deviation of the mode direction relative to the actuator force direction is pointed out as a key one in addition to modal mass and damping coefficient. In this context, the inherent differences between model order reduction by modal and by balanced truncation are being stressed. For the specific automotive vibration isolation application considered, the degradation of robust performance and stability is shown to be insignificant when obtaining a low-order controller by using total force feedback and neglecting flexibility in the design phase.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2006;129(2):193-201. doi:10.1115/1.2424972.

An alternative analysis technique, which does not require eigensolutions as a priori, for the dynamic response solutions, in terms of the transfer function, of one-dimensional distributed parameter systems with arbitrary supporting conditions, is presented. The technique is based on the fact that the dynamic displacement of any point in a waveguide can be determined by superimposing the amplitudes of the wave components traveling along the waveguide, where the wave numbers of the constituent waves are defined in the Laplace domain instead of the frequency domain. The spatial amplitude variations of individual waves are represented by the field transfer matrix and the distortions of the wave amplitudes at point discontinuities due to constraints or boundaries are described by the wave reflection and transmission matrices. Combining these matrices in a progressive manner along the waveguide using the concepts of generalized wave reflection and transmission matrices leads to the exact transfer function of a complex distributed parameter system subjected to an externally applied force. The transient response solution can be obtained through the Laplace inversion using the fixed Talbot method. The exact frequency response solution, which includes infinite normal modes of the system, can be obtained in terms of the complex frequency response function from the system’s transfer function. This wave-based analysis technique is applicable to any one-dimensional viscoelastic structure (strings, axial rods, torsional bar, and beams), in particular systems with multiple point discontinuities such as viscoelastic supports, attached mass, and geometric/material property changes. In this paper, the proposed approach is applied to the flexural vibration analysis of a classical Euler–Bernoulli beam with multiple spans to demonstrate its systematic and recursive formulation technique.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2006;129(2):202-208. doi:10.1115/1.2424974.

The physical model of this paper is an irregular enclosure with double flexible plates. The primary source is the vibration of Plate A excited by a point force. The secondary source is the vibration of Plate B excited by a polyvinylidene fluoride (PVDF) actuator. First, the interaction of the PVDF actuator and a thin plate is analyzed and the distribution of strain and stress is gained. Based on the hypothesis of linear distribution of strain on two sections of the plate–film system, a formula is deduced to calculate the rate of the strain distribution. Then an experiment is proposed to test the sound pressure response in an irregular enclosure under the excitation of the PVDF actuator. Second, the theoretical formulas of the mode contributions of the two plates and the cavity are deduced. Then the formulas are converted into compact matrix equations. Thus the expression of sound response of one point in the enclosure is gained under the excitation of both the primary and the secondary sources. Based on these results, the sound pressure square is taken as the control aim function. At last the optimized curves of control voltage and control phase are achieved.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2006;129(2):209-216. doi:10.1115/1.2424977.

The objective of this paper is to test and model a single-degree-of-freedom vibration isolation system with a magnetorheological (MR) foam damper under harmonic and random excitations. The results of this research are valuable for understanding the characteristics of the MR foam damper and include the experimental design and results of vibration mitigations for frequency ranges up to $2000Hz$. Transmissibility and acceleration hysteresis experiments of the MR foam damper system with different levels of input current are discussed. A simple damper design that eliminates many of the constraints normally associated with fluid filled devices is presented. Constitutive equations of the Bouc–Wen model are used to validate and characterize the MR foam damper. The motion characteristics of the MR foam damper are studied. Experimental results reveal that the mechanical behavior of the MR foam damper is nonlinear and that the field-dependent behavior of MR foam damper is associated with the applied frequency and acceleration amplitude. Experiments demonstrate MR foam damper works well in controlling vibrations and can be controlled and tuned for specific applications.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2006;129(2):217-229. doi:10.1115/1.2424978.

The effect of disabled fastening systems and ballast on railway vehicle derailment is investigated by developing a nonsymmetrical coupled vehicle/track model. In the model a half passenger car is considered, and modeled with a multi-body system with 18 degrees of freedom, which runs on a tangent track at a constant speed. The tangent track is modeled as two elastic beams by discrete nonsymmetrical supporters modeling fastening systems, sleepers, and ballasts. The normal contact forces between wheels and rails are described by Hertzian elastic contact theory, and the tangential forces by the nonlinear creep theory of Shen (Proceedings of the 8th IAVSD Symposium, Cambridge, MA, pp. 591–605). In the numerical analysis, the disabled rail fastening, rail pad, and ballast, on one and two sides of the track are, respectively, considered. Through a detailed analysis, derailment coefficients and the track state variations are obtained. The derailment coefficients are defined as the ratio of the lateral force to the vertical force of the wheel and rail (indicated by $L∕V$), duration of $L∕V$, and rate of the wheel load reduction (indicated by $ΔV∕V$), respectively. The variations of the contact points on the wheel treads, the track gauge, the track cross-level, and rail turnover angle are present in the paper. The numerical results obtained indicate that the failure of rail supports has a great influence on the vehicle running safety.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2006;129(2):230-238. doi:10.1115/1.2424979.

In active magnetic bearing (AMB) systems, stability is the most important factor for reliable operation. Rotor positions in radial direction are regulated by four-axis control in AMB, i.e., a radial system is to be treated as a multi-input multioutput (MIMO) system. One of the general indices representing the stability of a MIMO system is “maximum singular value” of a sensitivity function matrix, which needs full matrix elements for calculation. On the other hand, ISO 14839-3 employs “maximum gain” of the diagonal elements. In this concept, each control axis is considered as an independent single-input single-output (SISO) system and thus the stability indices can be determined with just four sensitivity functions. This paper discusses the stability indices using sensitivity functions as SISO systems with parallel/conical mode treatment and/or side-by-side treatment, and as a MIMO system with using maximum singular value; the paper also highlights the differences among these approaches. In addition, a conversion from usual $x∕y$ axis form to forward/backward form is proposed, and the stability is evaluated in its converted form. For experimental demonstration, a test rig diverted from a high-speed compressor was used. The transfer functions were measured by exciting the control circuits with swept signals at rotor standstill and at its $30,000$ revolutions/min rotational speed. For stability limit evaluation, the control loop gains were increased in one case, and in another case phase lags were inserted in the controller to lead the system close to unstable intentionally. In this experiment, the side-by-side assessment, which conforms to the ISO standard, indicates the least sensitive results, but the difference from the other assessments are not so great as to lead to inadequate evaluations. Converting the transfer functions to the forward/backward form decouples the mixed peaks due to gyroscopic effect in bode plot at rotation and gives much closer assessment to maximum singular value assessment. If large phase lags are inserted into the controller, the second bending mode is destabilized, but the sensitivity functions do not catch this instability. The ISO standard can be used practically in determining the stability of the AMB system, nevertheless it must be borne in mind that the sensitivity functions do not always highlight the instability in bending modes.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2006;129(2):239-251. doi:10.1115/1.2346694.

The performance of particle dampers whose behavior under broadband excitations involves internal friction and momentum transfer is a highly complex nonlinear process that is not amenable to exact analytical solutions. While numerous analytical and experimental studies have been conducted over many years to develop strategies for modeling and controlling the behavior of this class of vibration dampers, no guidelines currently exist for determining optimum strategies for maximizing the performance of particle dampers, whether in a single unit or in arrays of dampers, under random excitation. This paper focuses on the development and evaluation of practical design strategies for maximizing the damping efficiency of multi-unit particle dampers under random excitation, both the stationary and nonstationary type. High-fidelity simulation studies are conducted with a variable number of multi-unit dampers ranging from 1 to 100, with the magnitude of the “dead-space” nonlinearity being a random variable with a prescribed probability distribution spanning a feasible range of parameters. Results of the computational studies are calibrated with carefully conducted experiments with single-unit/single-particle, single-unit/multi-particle, and multiple-unit/multi-particle dampers. It is shown that a wide latitude exists in the trade-off between high vibration attenuation over a narrow range of damper gap size versus slightly reduced attenuation over a much broader range. The optimum configuration can be achieved through the use of multiple particle dampers designed in accordance with the procedure presented in the paper. A semi-active algorithm is introduced to improve the rms level reduction, as well as the peak response reduction. The utility of the approach is demonstrated through numerical simulation studies involving broadband stationary random excitations, as well as highly nonstationary excitations resembling typical earthquake ground motions.

Commentary by Dr. Valentin Fuster

### TECHNICAL BRIEFS

J. Vib. Acoust. 2006;129(2):252-255. doi:10.1115/1.2424983.

Experimental characterization of high dimensional dynamic systems sometimes uses the proper orthogonal decomposition (POD). If there are many measurement locations and relatively fewer sensors, then steady-state behavior can still be studied by sequentially taking several sets of simultaneous measurements. The number required of such sets of measurements can be minimized if we solve a combinatorial optimization problem. We aim to bring this problem to the attention of engineering audiences, summarize some known mathematical results about this problem, and present a heuristic (suboptimal) calculation that gives reasonable, if not stellar, results.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2006;129(2):256-259. doi:10.1115/1.2346695.

In this paper, study of nonhomogeneity as well as variable thickness in elliptic and circular orthotropic plates is undertaken. Nonhomogeneity of plate material is assumed to be a quadratic variation of Young’s modulii and density whereas shear modulus, is considered to vary linearly along both the axes. The quadratic thickness variation in orthotropic nonhomogeneous plates is also considered. Effect of variation of these parameters on vibrational characteristics are analyzed for various boundary conditions at the edges. Results are obtained using boundary characteristic orthogonal polynomials generated by using Gram-Schmidt orthogonalization procedure in Rayleigh-Ritz method.

Commentary by Dr. Valentin Fuster
J. Vib. Acoust. 2006;129(2):260-264. doi:10.1115/1.2345677.

Dry friction backward whirl is a self-excited vibration state in rotor-to-stator contact systems, by which the rotor is in continuous contact with the stator, slipping continuously on the contact surface and whirling backward at a supersynchronous frequency. To correctly cope the response of dry friction backward whirl, the effect of dry friction must be taken into account in rotor/stator models. From the knowledge on the characteristics of dry friction backward whirl, the whirl frequency, the existence condition and the solution of this response are derived analytically in this paper. The analytical results are verified by simulations and shown in good correspondence to the experimental observations.

Commentary by Dr. Valentin Fuster