Abstract
The scattering of time-harmonic plane longitudinal elastic wave by a large convex rigid object with statistical surface irregularities is considered. The maximum deviation of the corrugated surface from the smooth one is assumed to be small, and hence the boundary-perturbation technique is utilized in this study. First, the scattering of longitudinal wave by a large rigid sphere with statistical surface irregularities is treated as a canonical problem in the general discussion. It is found that the higher-order solutions can be obtained from the zeroth-order solution in a straightforward manner. Due to the complexity of the problem, only the first-order solution and its asymptotic expansion are explicitly computed and carried out. A general recipe based on the zeroth-order solution is given for the treatment of the general problem. The asymptotic expressions of mean values of the scattered wave function and the scattered intensity are also given for the general problem.
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