Transient Interactions of Spherical Acoustic Waves and a Cylindrical Elastic Shell

Abstract

The three-dimensional transient interaction between spherical acoustic waves with infinitely steep wavefronts and a circular cylindrical elastic shell of infinite length is investigated. The incident spherical wave is transformed into cylindrical partial waves by using the addition theorem for the modified Bessel function. The governing wave equation and equations of motion of the shell are solved by a series expansion-Laplace-Fourier transform technique. The transformed solution of the problem is obtained in closed form exact within the limit of series solution imposed by the Gibb's phenomenon. The physical solution is obtained by an accurate numerical scheme for the two-fold inverse Laplace-Fourier transforms. Detailed numerical results are obtained for the transient response of the shell and some quantitative effects of the sphericality of the incident waves on the response of the shell are also revealed.