Lamb waves in elastic–plastic plate containing voids

Abstract

Abstract Propagation of Lamb waves has been studied in an infinite plate of finite thickness and composed of elastic–plastic material containing void pores. The plastic deformation in the plate material is considered through a single-plane and direction. Assuming a linear relation between the elastic and plastic parts of the change in void volume fraction and using the stress-free boundary surfaces of the plate, the dispersion relations corresponding to the symmetric and antisymmetric vibrations with respect to the mid-plane of the plate are derived. The corresponding dispersion relations of Lamb modes in the elastic–plastic plate have been reduced by neglecting the presence of voids. Some earlier known results are recovered from the present formulation under particular cases. The behaviour of symmetric and antisymmetric family of Lamb modes are depicted pictorially against the frequency, slip-angle, thickness of the plate and void parameters in a specific plate material. It is found that the plasticity and the presence of the voids in the plate material affect the propagation of Lamb modes. In particular, at the slip-angle $45^o$, the $S_0$- and $A_0$- modes exhibit symmetry, but $S_0$ is bell shaped and $A_0$ is parabolic.