Evaluation of Planar Harmonic Impedance for Periodic Elastic Strips of Rectangular Cross Section by Plate Mode Expansion

Abstract

A system of periodic elastic strips (each one considered as a piece of a plate) is characterized by a matrix relation between the Bloch series of displacement and traction at the bottom side of the system. Both these mechanical fields are involved in the boundary conditions at the contact plane between the strips and the substrate supporting a Rayleigh wave. The analysis exploits the mechanical field expansion over the plate modes, including complex modes; numerical results satisfy the energy conservation law satisfactorily. The derived planar harmonic Green’s function provides an alternative tool for investigation of surface waves propagation under periodic elastic strips, with respect to pure numerical methods mostly applied in the surface acoustic wave devices literature. Perfect agreement of the presented theory with the experimentally verified perturbation model of thin strips is demonstrated.