Resonance theory of acoustic waves interacting with an elastic plate

Abstract

Sound transmission and reflection properties of an elastic layer immersed in a fluid are analyzed by extending the resonance formalism, previously developed by us for the case of a fluid layer [J. Acoust. Soc. Am. 65, 9–14 (1979)]. Resonance expressions for the transmission and reflection coefficients have been obtained both in terms of the frequency-thickness variable and of the angle-of-incidence variable. The resonance positions and widths are explicitly obtained from real equations in terms of given material quantities. Comparison of the resonance theory and exact calculations are given for a steel plate immersed in water. The resonance formalism results show excellent agreement with exact theory in all cases. Interferences between overlapping resonances are clearly identified and analyzed. An examination of the limiting form of the y resonances confirms previous empirical findings of other researchers concerning the frequency-thickness behavior of the poles and zeroes of the Rayleigh and Lamb resonances, and in particular the disappearance of Lamb modes and survival of one Rayleigh mode as the plate tends towards a half-space.