Analytical solution to vertical and rocking vibration of a rigid rectangular plate on a layered transversely isotropic half-space

This paper presents an analytical solution to the mixed boundary value problem for a dynamic rigid rectangular plate on the surface of a layered transversely isotropic half-space. For the contact problem, the mixed boundary conditions at the surface are converted into linear equations by means of Bessel series expansions. Solving these linear equations can get the expression of the contact stress, which can be further utilized to obtain the stresses and displacements of this model by the analytical layer element method of layered media. Additionally, the contact stresses can be used to evaluate the vertical and rocking compliances of a rectangular plate. A good agreement with existing solutions verifies the accuracy of the proposed method, and numerical examples are carried out to investigate the effect of angular frequency, length-to-width ratios, transverse isotropy and the stratification of media.