Waves in periodically structured media

Abstract

By the finite element method, the problem of steady-state wave motion in a 2-dimensional periodic medium is formulated in the form of a matrix eigenvalue problem. A matrix modification converts the large, sparse linear problem into a smaller, dense nonlinear matrix eigenvalue problem. The conversion makes the computation more efficient in data storage and in computing time. The dispersion curves of the lowest 10 modes are calculated. The propagation property of waves from the longest to modestly short wavelengths is discussed.