Reflection and transmission of steady state waves at a material interface between two waveguides

A boundary minimization and a variational method are developed for modal superposition solutions of semi-infinite elastic waveguides subjected to time harmonic boundary conditions. These results are then extended to obtain solutions for the reflection and transmission of steady state waves at a material interface between a homogeneous half-space and a laminated half-space. The boundary minimization method yielded a satisfactory match of the interface displacement and stress boundary conditions, although the rate of convergence was very slow. The interface solutions are seen to diverge when the variational procedure is used.