Point force excitation of a thick-walled elastic infinite pipe with an embedded inhomogeneity

The propagation of elastic waves in thick-walled pipe with an embedded inhomogeneity is considered. The pipe is excited by a point force applied on its surface and the time harmonic problem is solved using the null field approach, a method whose main characteristics are surface integral representations and expansions in spherical and cylindrical vector wave functions. Entering in the expression for the scattered field are the transition matrix for the cavity, the reflection matrices for the inner and outer surfaces of the pipe, the transformation functions between the spherical and cylindrical vector wave functions and also the translation for the cylindrical waves. Numerical examples, both in the frequency and time domain, are presented for a spherical cavity and an open circular crack.