forced rocking motion of a two -layer transversely isotropic half-space

A linear elastic transversely isotropic half-space coated by a transversely isotropic layer of finite thickness with different properties is considered as the domain of the problem. The axes of material symmetry of the layer and the half-space are considered to be parallel to each other and normal to the surface. A rigid circular plate is attached to the surface of the domain and affected by a rocking time harmonic vibration of constant amplitude. A relaxed boundary condition is assumed for the mixed boundary value problem. By using a scalar potential function, the equation of motion for both the coated layer and the underneath half-space are uncoupled. The governing equation for the potential function is determined to be a forth order partial differential equation. With the aid of Fourier series and Hankel integral transforms the PDE is solved and then the mixed boundary value problem is transformed to a set of dual integral equations, which in this paper are reduced to Fredholm integral equations of second kind. The Fredholm integral equations numerically solved. The validation is proved by comparing the results for the simpler case of isotropic homogeneous half-space.

کلیدواژه ها:

Surface rigid disc ، forced rocking vibration ، transversely isotropic ، two layerhalf-space ، dual integral equations ، soil-structure-interaction