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The Quarterly Journal of Mechanics and Applied Mathematics 1976 29(4):527-546; doi:10.1093/qjmam/29.4.527
© 1976 by Oxford University Press
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SCATTERING OF SOUND WAVES BY FINITE MEMBRANES AND PLATES NEAR RESONANCE

F. G. LEPPINGTON

( Mathematics Department, Imperial College London )

A flexible membrane (or thin elastic plate) of finite width and infinite length is set in an infinite rigid plane baffle and is irradiated by a time-harmonic sound wave. It is required to find the form of the scattered field when the fluid is relatively light compared with the mass of the vibrating panel. In this low fluid-loading limit a simple estimate for the panel deflection, and hence for the velocity potential field, is obtained on the basis of an equation for a membrane (or plate) vibrating in vacuo. This approximation is not uniformly valid, since it fails at the eigenvalues of the approximating membrane (or plate) equation when radiation damping is ignored. An improved first estimate is obtained, to take account of the small but non-zero radiation damping in the system. The method is also used for the corresponding three-dimensional, axially symmetric problem of a circular membrane. The results agree with independently obtained estimates for the case when the membrane (or plate) is large.


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