Nonlinear Love Waves in Elastic Media

Abstract

The horizontally polarized shear elastic waves are of interest in seismology and engineering. A. E. H Love proved the existence of such waves in a homogeneous elastic layer overlying an elastic half-space. In this thesis, we first discuss Love waves in an isotropic layer overlying an inhomogeneous elastic half-space and obtain the dispersion relation in the layer. The dependence of phase velocity on the wave number is displayed graphically. Next, we consider an anisotropic layer overlying an anisotropic half-space. The dispersion relation satisfied by Love wave is obtained in this case. This dispersion relation reduces to the one for isotropic case. Also for an inhomogeneous anisotropic layer overlying an anisotropic half space we obtain the dispersion relation in a determinant form. The case of Love waves in the nonlinear model of the media is studied in the end. The stress-strain relation now involves a potential. We use the Murnaghan model and we consider a typical Love wave problem with added assumption of nonlinear deformation. The resulting nonlinear wave equation in terms of the displacements with both linear parts and nonlinear parts is studied using perturbation method