Free-field wave motion in an inhomogeneous elastic half-plane with surface elasticity effects

Abstract

Elastic wave propagation in аn inhomogeneous half-plane with surface elasticity effects is studied in this paper. All three types of travelling body waves are considered, namely pressure, vertically polarized shear and horizontally polarized shear waves propagating under time-harmonic conditions. Along the half-plane boundary, a localized constitutive law within the framework of the Gurtin-Murdoch theory is introduced, resulting in non-classical boundary conditions as opposed to the simple traction-free conditions of classical elasticity. The free-field wave motion is analytically derived here by using the wave decomposition technique, in conjunction with appropriate functional transformations for the displacement vector. Next, a series of parametric studies serves to identify the differences in the free field motion between that for the inhomogeneous half-plane with surface elasticity and the reference case of a homogeneous material with a traction-free surface. Finally, the dependence of the free-field wave motion as it develops in the material on the level of inhomogeneity and on the magnitude of the localized surface elasticity parameters, as well as on the type of travelling waves, is quantified in this work.