Mathematical boundary integral equation analysis of an embedded shell under dynamic excitations

A boundary integral equation method is presented for the analysis of a thin cylindrical shell embedded in an elastic half-space under axisymmetric excitations. By virtue of a set of ring-load Green's functions for the shell and a group of dynamic fundamental solutions for the semi-infinite medium, the structure–medium interaction problem of wave propagation is shown to be reducible to a set of coupled boundary integral equations. Through the analysis of an auxiliary pair of Cauchy integral equations, the singularities of the contact stress distributions arc rendered explicit. With a direct incorporation of such analytical features into the formulation, an effective computational procedure is developed which involves an interpolation of regular functions only. Typical results for the dynamic contact load distributions, displacements, and complex compliance functions are included as illustrations. In addition to furnishing quantities of direct engineering interest, this treatment is apt to be useful as a foundation for further rigorous as well as approximate developments for various related physical problems and boundary integral methods.