Interaction of rocking vibration of a buried rigid circular disc and a two-layer transversely isotropic half-space

A linear elastic layer of finite thickness bonded on a half-space each containing a transverselyisotropic material is considered. a rigid circular disc attached to the interface of these two domains isconsidered to be affected by a rocking vibration of constant amplitude. with the aid of a scalar potentialfunction, the equations of motion in each domain are solved using fourier series and hankel integraltransforms. because of the involved integral transforms, the mixed boundary value problem is changedto dual integral equations; which are reduced to fredholm integral equations. because of the complexintegrand function existing in the dynamic case, analytical solution cannot be given in general. however,a closed-form solution is introduced for the static case, which itself degenerates to the solution for anisotropic case existing in the literature. the contact stress in between the rigid disc and the surroundingmedia, and the related impedance function are analytically determined in the static case. with thehelp of contour integration, the governing fredholm integral equations are numerically evaluated in thedynamic case. the dynamic contact pressure and the impedance function are numerically evaluated ina general dynamic case. the shape induced singularity in the contact pressure is investigated in detail.some numerical evaluations are given for different transversely isotropic materials to show the effect ofanisotropy.