Dispersion of elastic waves in an inhomogenous multilayered plate over a Winkler elastic foundation with imperfect interfacial conditions

Abstract

This study examines the dispersion of elastic waves in a strongly inhomogeneous three-layered plate resting on a Winkler elastic foundation in the presence of imperfect interfacial conditions alongside a stress-free upper face. The propagation of elastic waves in the plate is governed by the two-dimensional anti-plane shear motion. The asymptotic technique is employed for the analysis. The exact dispersion relation and the overall cut-off frequency are determined. Within the long-wave low-frequency region, the shortened polynomial dispersion relation corresponding to the exact dispersion relation has been computed and studied for a particular material contrast. The associated one-dimensional equations of motions are also derived in approximate forms for perfect interface as a case of interest. Finally, according to the findings of this investigation, the obtained approximate equations of motions for a three-layered plate remain valid over the entire low-frequency spectrum even in presence of an elastic foundation. We also examined the variational impacts of the dimensionless Winkler elastic foundation parameter G and the interface imperfect parameter γ on the dispersion branch of harmonic waves. Furthermore, to assure the long-wave low-frequency range, the numerical simulations and graphical visualization are presented by utilizing certain physical data.