Boundary integral equations from Hamilton´s principle for surface acoustic waves under periodic metal gratings

The procedure describes the derivation of boundary integral equations for surface acoustic waves propagating under periodic metal strip gratings with piezoelectric films. It takes into account the electrical and mechanical perturbations, including the effects of mass loading caused by the gratings with an arbitrary shape. First, an integral equation is derived with line integrals on the boundaries within one period. This derivation is based on Hamilton´s principle and uses Lagrange´s method of multipliers to alleviate the continuous conditions of the displacement and the electric potential on the boundaries. Second, boundary integral equations corresponding to each substrate, piezoelectric film, metal strip, and free space region are obtained from the integral equation using the Rayleigh-Ritz method for admissible functions. With this procedure, it is not necessary to make any assumptions for separation of the boundary conditions between two neighboring regions. Consequently, we clarify the theoretical basis for the analytical procedure using boundary integral equations for longitudinal LSAW modes.