Dynamic analysis of an elastic plate on a cross-anisotropic elastic half-space under a rectangular moving load

The dynamic response of an elastic thin plate resting on a cross-anisotropic elastic half-space to a rectangular load moving on its surface with constant speed is analytically obtained. The moving load and the plate and soil displacements are expanded in double complex Fourier series involving the two horizontal coordinates x and y as well as the time and the load velocity. Thus, the plate equation of lateral motion reduces to an algebraic equation, while the soil equations of motion reduce to a system of three ordinary differential equations with respect to the vertical coordinate z, which can be easily solved. Compatibility and equilibrium at the plate–soil interface as well as employment of the boundary conditions of the system enable one to determine the solution in terms of displacements of the plate and the half-space soil medium. The solution is first verified by using it to obtain as special cases the solutions for isotropic and cross-anisotropic half-space problems and compare them against existing analytical solutions. Parametric studies are conducted to assess the effects of the degree of cross-anisotropy on the plate and soil responses in conjunction with the effects of other important parameters, such as the speed of the moving load.