Dynamic response of an elastic plate on a transversely isotropic viscoelastic half-space with variable with depth moduli to a rectangular moving load

Abstract

The dynamic response of a flexural elastic plate on a transversely isotropic half-space with elastic constants varying with depth to a rectangular load moving with constant speed is determined analytically. Soil viscoelasticity via hysteric damping and plate viscous damping is also considered. Use is made of the method of the complex Fourier series involving the two horizontal coordinates and the time. Because the load speed is constant, only a double series expansion of the response functions is required. 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. Use of boundary conditions and equilibrium and compatibility at the soil-plate interface help to determine the constants of integration and obtain the soil and plate response in closed form. Verification of the obtained solution is done by using it to determine the response of simpler cases to moving loads for which there are analytical results in the existing literature. Parametric studies are finally conducted to assess the effects of viscoelasticity, cross-anisotropy and non-homogeneity of soil, of stiffness of the plate, as well as of load speed on the plate response.