The plane wave expansion method applied to thin plates

Abstract

The plane wave expansion method refers to a computational technique in electromagnetics to solve Maxwell's equations. This method is popular in the photonic crystal community, because it is possible to obtain the band structure (dispersion-relation) of photonic crystals with specific forms. Since photonic crystals are periodic systems, the method expands all parameters crystal in Fourier series (plane waves). These expansions transform the wave equation in an eigenvalue equation. In this work, we will follow the line of previous investigations where the plane wave method was applied to the classical theory of thin plates. In particular the plane wave expansion method will be applied to the Mindlin equation. This equation describes the out-of-plane vibrations of thin plates in a better way—the classical theory of thin plates.