Three-dimensional guided waves in laminated composite plates excited from point source

Abstract

Three dimensional wave propagation characteristics in laminated plates are studied considering this anisotropic and viscoelastic properties of fiber reinforced composite material. A Rayleigh-Ritz based stiffness method is used to discretize the plate in the vertical direction to determine propagation characteristics (wave number, phase velocity, group velocity) and mode shapes for a plane wave front. For 3-dimesional cases, wave propagation problem is decomposed into a series of two-dimensional plane wave problems with three displacements coupled. Double Fourier transform integral transformations are used to get the governing equation in a transformed wave number domain. Steady state elastodynamic Green's functions for the laminated composite plates are constructed through summing the contribution of all two-dimensional problems and the application of modal summation technique. Numerical integration of double infinite integrals is performed by summations over a finite range. The wave propagation characteristics for a 16-layer unidirectional fibre reinforced laminated composite plate show the orthotropic nature of the plate reflected in its 3-D wave propagation characteristics. It is also seen that the Green's functions for 3D waves are very different from those for plane strain 2D waves. Furthermore, the direction of propagation has a significant effect on the Green's function for surface displacements.