Resonant acoustic scattering from solid targets

Abstract

An asymptotic method of solution is presented for scattering of acoustic waves from solid elastic targets. The asymptotic parameter is the ratio of the fluid density to that of the solid, and the solution is developed using the method of matched asymptotic expansions in this small quantity. The perturbations to the background rigid scattered field are regular for frequencies away from the frequencies of free vibration of the target in vacuo, but, near these frequencies, the perturbation is singular in that an asymptotically small value of the density ratio produces a change in the scattered field of order unity. By combining the regularly and singularly perturbed expansions, a solution is obtained that is uniformly correct at all frequencies. The elements in the uniform solution depend only upon the in vacuo modes and frequencies, and the Green’s function for the equivalent rigid target. At no stage is it necessary to solve the fully coupled system. An analysis of the asymptotic approximation for a spherical target shows that it is equivalent in the high-frequency limit to the approximation predicted by resonance scattering theory.