Wave Propagation in an Infinite Elastic Plate in Contact with an Inviscid Liquid Layer

Abstract

The dispersion relation for straight-crested waves in an isotropic plate in a state of plane strain that is covered by a layer of an incompressible liquid is derived and investigated in the limits of very long wavelengths (thickness-stretch vibrations of the plate-liquid system) and of very short wavelengths (surface waves and the solid-liquid interface). In the case of surface waves, there are two dispersive modes, one predominantly elastic (analogous to Rayleigh waves) and the other essentially fluid, and in the thickness-stretch case, there are an infinite number of essentially elastic modes and one fluid mode. An approximate version of the dispersion relation valid for arbitrary wavelength is obtained by using two nonclassical plate theories to account for the extensional and flexural deformations of the plate. This relation gives rise to five modes on the real branch, which are identified as being thickness-stretch, thickness-shear, flexural, extensional, and fluid in character, and three modes on the imaginary branch, namely, flexure, thickness-shear, and thickness-stretch. Two of the five cutoff frequencies are modified by the presence of the liquid layer. A variety of numerical results are presented in graphical form.