Dynamic analysis of an elastic plate on a cross-anisotropic and continuously nonhomogeneous viscoelastic half-plane under a moving load

The dynamic response of an elastic thin plate to a load moving on its surface with constant velocity is determined analytically. The plate rests on a cross-anisotropic and continuously nonhomogeneous viscoelastic half-plane soil medium. Soil nonhomogeneity is associated with elastic moduli increasing with depth. Viscoelastic effects are introduced via the hysteretic damping model. The solution of the problem is obtained with the aid of the complex Fourier series method involving the horizontal coordinate x and the time t. Thus, the governing partial differential equations of motion for the plate-soil system are reduced to an algebraic equation for the plate and a system of two ordinary differential equations with variable coefficients for the soil. This system is solved analytically by the method of Frobenius. Compatibility and dynamic equilibrium at the plate-soil interface as well as boundary conditions at the plate surface and at infinite soil depth enable one to finally obtain the response for both the plate and the soil analytically. Verification of the solution is done by means of comparisons with the known existing analytical solutions for the special cases of isotropy and homogeneity with or without the plate. Parametric studies are finally performed, and the effects of soil anisotropy, nonhomogeneity and damping on the plate and the supporting soil are assessed.