Acoustic scattering by baffled membranes

Abstract

A flexible membrane is set in an infinite plane baffle. The plane separates an acoustic field from a vacuum. A time harmonic wave is incident from the fluid on the membrane. When the frequency of the incident wave is not close to an in-vacuo resonant frequency of the membrane, the reaction of the fluid on the membrane is small. However, near a resonant frequency the fluid–membrane coupling is significant. We use the method of matched asymptotic expansions to obtain an asymptotic expansion of the scattered field. It is uniformly valid in the incident frequency. The expansion parameter ε≪1 is the ratio of the fluid and membrane densities. The outer expansion, valid away from resonance, is O(ε). The inner expansion, valid near resonance, is of order unity. The fluid loading is shown to have the effect of decreasing the resonant frequencies from those of the in-vacuo membrane. Simple and double resonant frequencies are analyzed. However, the method is applicable to higher order resonant frequencies. Finally, the method is applied to normal incidence of a plane wave on a circular membrane.