Propagation and scattering of elastic waves in transversely isotropic plates

In this work we consider the propagation and scattering of Lamb waves in a uniaxial fiber-reinforced plate. The composite material is modeled as homogeneous and transversely isotropic with the symmetry axis parallel to the fibers, which are parallel to the free surface of the plate. The exact dispersion relation for an arbitrary direction of propagation in this homogeneous anisotropic plate is developed. In addition, a numerical scheme to determine the dispersion relation for a multi-layered plate composed of uniaxial or cross ply lay-ups has been investigated. The exact dispersion equation has been used to investigate the dispersion of guided waves in uniaxial graphite fiber reinforced magnesium plate. We also present, using the numerical scheme, dispersion of waves in a cross-ply Gr/Epoxy plate. Scattering of guided (Lamb) waves in a uniaxial fiber-reinforced composite plate by surface breaking and symmetrically buried cracks is then investigated in this thesis. Scattering of the different Lamb modes by cracks of different lengths is analyzed using a hybrid method combining the modal representations (obtained by the numerical scheme) of the transmitted and reflected fields with the finite element representation of the field near the crack. Results are presented showing the variations of the transmission and conversion coefficients with the frequency of excitation and the length of the crack. Some results are presented for the time domain response of the transmitted field when a line load is applied on the surface of the plate. For this purpose only the first symmetric propagating mode generated by the line load is considered. The depth of the crack is seen to influence the reduction in the amplitude of the time response.