Analytical/Numerical Solutions to the Problem of the Dynamic Response of an Elastic Plate on a Continuously Non-Homogeneous Cross-Anisotropic Viscoelastic Soil to a Moving Load

Abstract

In this work the problem of the dynamic response of a flexural elastic plate on a continuously nonhomogeneous viscoelastic cross-anisotropic half-plane or half-space soil medium to a line or rectangular load moving with constant speed is determined analytically/numerically. Soil nonhomogeneity is associated with elastic moduli increasing with depth. Plate viscous damping is considered, and the viscoelastic effects of the soil are introduced via hysteric damping. The solution of the problem is obtained with the aid of the complex Fourier series method involving the horizontal coordinates and the time. Employment of this method reduces the partial differential equations of motion for the soil and the plate to ordinary differential equations with variable coefficients and an algebraic equation, respectively. Those ordinary differential equations are solved by the method of Frobenius. Verification of the solutions is done by means of comparisons with known existing analytical solutions for the special cases of isotropy and homogeneity with or without the plate.