Keele Research Repository

The propagation of waves along elastic half-spaces and plates has long been an active research area with lots of applications in seismology andmodern industries. Much attention has been paid to the study of wave propagation in a linear isotropic solid with traction-free or fixed boundary conditions. However, much more investigation is deserved for anisotropic solids under other type of boundary conditions, or even a solid with a hump on its surface.

The purpose of the thesis is to investigate the influence of the elastic property and profile of propagation media and boundary conditions on wave speeds, and predict the wave speed in various situations. Chapter 1 is devoted to introducing the governing equations and several specific materials used as examples in subsequent analysis. Chapter 2 is concerned with the propagation of free surface waves on an elastic half-space that has a localized geometric inhomogeneity perpendicular to the direction of wave propagation (such waves are known as topography-guided surface waves). We use the Stroh formalism to examine how such hump modifies the surface wave speed slightly on an anisotropic elastic half-space. In Chapter 3, an asymptotic model is constructed to predict the speed of waves propagating along a thin elastic plate with elastically restrained boundary conditions (ERBC). The Stroh formalism is again applied to deal with general anisotropy, which can be specified later to analyze the case of linear isotropy and the transverse isotropy. Chapter 4 deals again with the case of a thin plate with ERBC as in the previous chapter, but the effects of pre-stress and the condition of incompressibility are also considered.