Uniqueness of Solutions to Variationally Formulated Acoustic Radiation Problems

[+] Author and Article Information
Xiao-Feng Wu

Department of Mechanical Engineering and Institute for Manufacturing Research, Wayne State University, Detroit, MI 48202

Allan D. Pierce

Graduate Program in Acoustics, Pennsylvania State University, University Park, PA 16802

J. Vib. Acoust 112(2), 263-267 (Apr 01, 1990) (5 pages) doi:10.1115/1.2930121 History: Received March 01, 1989; Online June 17, 2008


Determination of the surface acoustic pressure given the surface velocity of a vibrating body can be formulated in various ways. However, for some such formulations such as the surface Helmholtz integral equation, solutions are not unique at certain discrete frequencies. Such uniqueness problems can also be present for variational formulations of the problem, but the variational formulation based on the normal derivative of the Kirchhoff integral theorem has unique solutions for vibrating disks and plate-like bodies. For bodies of finite volume, but for which each surface point is vibrating in phase, the total radiated acoustic power is always unique, even though the pressure may not be. The latter conclusion is supported by numerical calculations based on the Rayleigh-Ritz technique for the case of a finite cylinder vibrating as a rigid body in the axial direction.

Copyright © 1990 by The American Society of Mechanical Engineers
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