Volume 113, Issue 4, April 2003
Index of content:
- STRUCTURAL ACOUSTICS AND VIBRATION 
On the dynamic stiffness of preloaded vibration isolators in the audible frequency range: Modeling and experiments113(2003); http://dx.doi.org/10.1121/1.1557214View Description Hide Description
The nonlinear, preload-dependent dynamic stiffness of a cylindrical vibration isolator is examined via measurements and modeling within an audible frequency range covering 50 to 1000 Hz at various preloads. The stiffness is found to depend strongly on frequency—resulting in peaks and troughs, and on preload—particularly above 500 Hz. The problems of simultaneously modeling the rubber prestrain dependence and its audible short-term response are removed by adopting a nearly incompressible materialmodel, being elastic in dilatation while displaying viscoelasticity in deviation. The latter exhibits a time strain separable relaxation tensor with a single function embodying its time dependence. This function is based on a continuous fractional order derivative model, the main advantage being the minimum number of parameters required to successfully model the rubber properties over a broad structure-borne sound frequency domain, while embodying a continuous distribution of relaxation time. The weak formulations corresponding to the stiffness problem are solved by an updated Lagrangian nonlinear finite-element procedure. The model and measurement results agree strikingly well with static and dynamic measurements throughout the whole frequency domain for the examined preloads.
113(2003); http://dx.doi.org/10.1121/1.1558374View Description Hide Description
A novel substructure coupling technique based on the proper orthogonal decomposition method is presented for the midfrequency range vibration of linear dynamical systems with parameter uncertainty. For a given frequency band, the methodology permits the derivation of an adaptive basis for each subsystem and the construction of a reduced-order model of the global structure. The formulation is directed toward the efficient probabilistic characterization of model-based predictions in the framework of a stochastic finite element method. The efficiency of the substructure method has been contrasted both from the viewpoint of adopting free–free and fixed–fixed substructure proper orthogonal modes in order to arrive at a reduced subsystem model. The distinction as well as similarity of the present methodology with the component mode synthesis is also pointed out. The proper orthogonal modes are obtained from both frequency- and time-domain approaches, and their suitability is discussed in relation to the behavior of a specific system. The substructure approach elegantly integrates with a version of stochastic finite elements based on orthogonal decompositions and projections of stochastic processes.
113(2003); http://dx.doi.org/10.1121/1.1553456View Description Hide Description
The equations of in-plane vibration in thin flat plates are solved for free vibration in circular plates clamped at the outer edge. The mode shapes are represented by trigonometric functions in the circumferential direction and by series summation of Bessel functions in the radial direction. Accuracy of the predictions of natural frequencies and mode shapes is assessed by comparisons with finite-element predictions and with previously reported results. The present solution gives very accurate predictions. The work also highlights the nature of coupling between the different circumferential and radial modes and the response of different vibrational modes at the center of the plate. It is shown that the center point of the plate vibrates only for modes with unity circumferential wave number (number of nodal diameters). Nondimensional frequency parameters are listed and the radial mode shapes of natural vibration are depicted to illustrate the free-vibration behavior in the frequency range of practical interest.
113(2003); http://dx.doi.org/10.1121/1.1515791View Description Hide Description
This analysis is concerned with the calculation of the elastic wavetransmission coefficients and coupling loss factors between an arbitrary number of structural components that are coupled at a point. A general approach to the problem is presented and it is demonstrated that the resulting coupling loss factors satisfy reciprocity. A key aspect of the method is the consideration of cylindrical waves in two-dimensional components, and this builds upon recent results regarding the energetics of diffuse wavefields when expressed in cylindrical coordinates. Specific details of the method are given for beam and thin plate components, and a number of examples are presented.
113(2003); http://dx.doi.org/10.1121/1.1555612View Description Hide Description
The sound radiation from a vibrating rail can be predicted using a two-dimensional model under certain conditions. This paper explores these conditions and shows that, if the decay rate of vibration along the rail becomes large or the wavelength in the rail becomes small, it becomes necessary to allow for three-dimensional radiation characteristics. In practice, however, noise from a rail can be predicted using a two-dimensional model for frequencies above about 250 Hz, and even where three-dimensional effects become important, these can be allowed for by simple correction terms. When the wavelength in the rail approaches that of acoustic waves in air, the angle between the direction of sound radiation from the rail and the normal to the rail increases, in some cases to more than 45°. This must be accounted for if the performance of noise barriers is to be calculated using a two-dimensional approach.