Transient response of an elastic shell to an acoustic impulse using Green's theorem

Abstract

The transient response of a sphere subjected to an incident acoustic impulse is studied by the boundary integral method. The problem is reduced from three dimensions to one independent variable on the shell's surfaces by use of the free-space Green's function. Three different shell models are used: (1) a rigid shell, for which the normal derivative of the pressure at the surface is zero, (2) a single surface thin shell for which Green's theorem is applied only to the fluid pressure since the thin shell equations model the surface dynamics, and (3) a two surface thick shell for which Green's theorem must also be applied to the curl and the divergence of the solid displacement vector. The surface is discreetized and the problem is numerically integrated in time. The state variables are related by finite differences. The results are compared to those of previous studies. The rigid shell problem gives good agreement. Numerical instabilities in the elastic shell solutions are discussed.