Modal Representation of Two-Dimensional Elastodynamic Green's Functions

Green's functions for a laminated composite plate have been studied using the representation in terms of guided modes. Attention has been focused here on the two-dimensional (plane strain) motion. For this purpose, the exact dispersion equation for the laminated plate has been solved using Muller's method, and initial estimates obtained through a stiffness-based Rayleigh-Ritz type approximate technique. The well-known numerical difficulties associated with computation of eigenvalues and eigenmodes at high frequencies are circumvented by adopting the delta matrix technique. Numerical results for an isotropic plate are compared with those obtained from the evaluation of the wave-number integrals. Results are presented also for a 35-layer cross-ply composite plate.