The Radiation of Love Waves from an Oscillating Cylinder

Abstract

We consider the radiation of Love waves from a rigid circular cylinder imbedded part way into the upper solid layer overlying a semi-infinite solid and oscillating sinusoidally about its vertical axis. Only the radial component of the vector potential exists, and this is transformed into a scalar potential satisfying Helmholtz's equation; the boundary conditions are unusual for propagation in a fluid. Because the boundary values on the cylinder are mixed and the cylinder is finite in length, the mathematical formulation is converted into a pair of integral equations by means of a Green's function. The latter is obtained in two ways: using Hankel transforms, and using Weyl expansion for the source. In either case, the final integration is obtained by closing a contour. The contributions from the poles have the characteristics of Love waves. The contributions from the deformation of the contour about branch cuts have the property of lateral waves. The evaluation of the Green's functions on the surface of the cylinder enables us to replace the dual integral equations approximately by two sets of simultaneous algebraic equations for the unknown wavefield or its normal derivative. Lastly, the Green's integral is integrated numerically.