Wave propagation in elastic material with voids

Abstract

The study of wave propagation in elastic materials containing uniform distribution of small voids has been presented. Two different types of surface waves, namely, Rayleigh waves and Love waves have been investigated for different models. The mathematical analysis of motion and deformation in the problems has been done by employing the mathematical techniques namely, Haskell Matrix method and Effective boundary condition method. newlineThe dispersion relations for Rayleigh-like and Love-type surface waves propagating in a multilayered medium composed of elastic solids containing uniform distribution of voids with welded contact in each subsequent interface have been derived using Haskell matrix method. It is found that Rayleigh-like waves are dispersive in nature and the particles have elliptically retrograde motion. For Love-type waves progressing in the model, there exist two wave fronts propagating with distinct speeds that are dispersive in nature. One of these wave fronts is analogous to that obtained for multilayered elastic solid, while the other front is new that appears due to the presence of voids. The numerical computations have been performed to observe the effect of voids on the speed of these surface waves for 2-layered and 3-layered models. newlineThe propagation of Rayleigh-like surface waves in an elastic solid half-space coated with a thin elastic solid, both containing voids has been explored for two different types of the interfaces. The thin coating/layer has been considered to be either in welded or smooth contact with the substrate. By employing effective boundary condition method, an approximate secular equation of up to fourth-order in terms of wavenumber for the corresponding model has been derived. The effect of voids and nature of interface in the model has been investigated numerically. newline newline