Scattering of Transient Elastic Waves by a Circular Cylindrical Cavity

摘要

Two problems of transient wave scattering from a circular cylindrical cavity in an infinite elastic solid are considered. In the first of these, the cavity wall is subjected to a suddenly applied concentrated line load. In the second, a transient plane compressional wave impinges on the cavity wall. Formal solutions in the form of a series of Fourier integrals are written for both problems by employing a double-integral transform (Laplace for time t , Fourier for circumferential coordinate theta), the integrals representing theta -traveling waves governed by particular branches of the underlying frequency equation. In particular, the Rayleigh waves on the cavity surface, corresponding to a limiting high-frequency large wave number pair, are evaluated. They are found to be spatially theta -independent waves, nondecaying, and periodic (2pi) in time, which predominate in the long-time solutions, producing sizeable disturbances that have not been previously noted and assessed. (Author)