Two-dimensional boundary element analysis of quartz surface wave resonators

In this paper we present the 2D fundamental solutions for the time-harmonic dynamic problems of piezoelectric materials. Given a time-harmonic line force or charge at the origin of an infinite piezoelectric solid, we derive the displacement and electric potential at an arbitrary point. The solution, obtained using the Radon transform, has an interesting feature that it can be split into two parts: singular static and regular dynamic parts. The singular static part corresponds to the static fundamental solution and the regular dynamic part provides frequency dependency. The regular part is presented in a form suitable for numerical evaluation. The implementation of the fundamental solutions into the boundary element method (BEM) for the eigen frequency problems of the surface wave resonators is outlined along with key technical features required for the successful BEM analysis.