885095973

developed to increase the understanding of thc noise gencrated from engine drive chains. [Work supported by General Motors Corporation.]

11:05

2SA9. Behayior of multiple degree of freedom system* havfng neighboring eigeny&lues: Veering of tbe eigenvaJoe loci and high modę sensitirity. Pei-Tai Chen and Jerry H. Ginsberg (School of Mech. Eng., Georgia InsL of Technol., Atlanta, GA 30332)

Interesting phenomena occur w hen lincar Systems contain natural frequencies that become close as a system parameter is altered. The behavior of eigenfunctions and eigenvalues is studied by applying a perturbation analysis to a self-adjoint system. Veering of the cigenvalue loci versus the smali perturbation parameter is observed and thc critc-rion for the occurrence of yeering is identified. It is proven that in the veering region, the eigenfunctions are highly sensitive to the value of the system parameter. A corollary is that in a system, whose individual subcomponents are highly coupled and nearly identical, eigeiwalue yeering and high modę sensitivity are associated with modę localization, in which some of the system modes are strongly enhanced in a smali portion of the domain. An example of a previously studied two-span beam with irregular spacing of the supports displays the corrclation and modę localization, the high modę sensitivity, and yeering of the eigen-value loci. Results of the perturbation analysis are shown to be virtually identical to those of the cxact solution of the equations of motion. [Work supported by the Office of Nava! Research, Codę 1132-SM.]

11:20

2SA10. Natural frequencies and bending modę shapes of thin perforated plates using a yariational raethod. Oliyier Beslin, Pascal Millot (Laboratoire des Sciences de PHabitat, Ecole Nationale des Travaux Publics de 1’Etat, 69518 Vaulx-en-Velin, France), and lean-Louis Guyader (Laboratoire Acoustique et Vibrations, Institut National des Sciences Appliąuees, 69621 Villeurbanne, France)

A theoretical method to predict eigenfrequencies and modę shapes of a perforated piąte was developcd by building its Hamiltonian as a functional of the displacemcnt field. The displacement functional base was chosen to be thc natural base of a nonperforated piąte having the same geometrical and mechanical characteristics as the perforated one with simply supported bouudary conditions. Limiting the base vectors to a finite number, the extremization of the Hamiltonian was trans-formed into a Rayleigh-Ritz problem. Formulas of this analytical de-yelopment were implemented on a Computer to solve the eigenvalue problem for any kind of rectangular perforations. Numerical singulari-tics were encountered, regarding the holes’ shapes and sizes, and vector sets. They were removed by using some simple physical considerations. The program dcveloped for this study was tested by treating special cases, well known in the literaturę. For example, the case of a fuli piąte with free boundary conditions was simulated by introducing a crown of holes around the edges of the piąte, setting it free of its supports. Several cases of perforated plates were also computed. This work is the first part of a morę generał study on sound radiation from plates with holes and perforations.

11:35

2SA11. Matched asyroptotic expansions solution for low-frequency sound radiation from fluid-loaded, baffłed plates. Chris tiaan Kauffmann (Faculty of Technical Math. and Informatics, Delft Univ. of Technol., P.O. Box 356, 2600 AJ Delft, The Nethcrlands)

The method of matched asymptotic expansions is used to investigate sound radiation from fluid-loaded, baffled, thin elastic plates of dimen-sions smali compared to the acoustic wavelength, i.e., for k_<3a-<\, where ko is the acoustic wave number and a is a typical size of the platc. In this low-frequency region both near-field quantities (piąte response and sur-face pressures) as wcll as far-ficld radiation properties are obtained. Al Iow frequencies, the piąte radiates sound likc a monopole, the strength of it bcing proportional to the net volume yelocity of the platc. The consistency of the method is tested by power balance considerations that are shown to be valid up to leading order. [Work supported by the TNO Instiłute of Applied Physics, Delft, The Netherlands.]

11:50

2SA12. Ioput mobilities and power flows for edge excited, semi-infinite plates. Christ iaan Kauffmann (Faculty of Technical Math. and Informatics, Delft Univ. of Technol., P.O. Box 356, 2600 AJ Delft, The Netherlands)

This paper relies highly on a paper by E. Eichler [J. Acoust. Soc. Am. 36, 344 (1964)], which contains an analysis of the response of a semi-infinite, thin platc excited by a time-harmonic load applied at a stud of width la attached to the edge, the rcmainder being free. Kichler used spatial Fourier transforms in the edge direction to obtain closed form integral expressions for the piąte response. The presenl paper pro-yides fuli details on thc analysis (some of them not yet published) and presents new expressions for the input power fed into the piąte. Numerical results covering a wide rangę of ka are presented, allowing for a simple physical interpretation in three cases: (a) ka< 1: point excitation, (b) ka— co: linę (or beam modę) excitation, and (c) ka = 0(1): in-terference effects at intermediate frequencies, which are also present in the simple acoustical analogy of a baffled piston. [Work supported by the TNO Institute of Applied Physics, Delft, The Netherlands.]

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J. Acoust Soc. Am., Vol. 89, No. 4, Pt 2, April 1991

121st Meeting: Acoustical Society of America

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