Response of rigid circular plate in a functionally graded transversely isotropic, half-space under horizontal steady-state excitation

In this paper, a theoretical formulation for lateral translation and impedance function of a rigid foundation in a transversely isotropic functionally graded (TIFG) half-space is presented. Accordingly, the medium is considered linear elastic and the elastic constants of materials vary exponentially along the depth for considering the effect of elastic non-homogeneities. The relax treatment of mixed boundary value problem is formulated by integrating the transformed kernels of Green's functions over the foundation area with unknown surface traction function, which can be reduced into a Fredholm integral equation. The results represent the impact and treatment of frequency and material anisotropy through the medium. In addition, static and dynamic distribution of tangential shear stress over the foundation for surface and embedded disk extracted and the cutoff frequency is found out explicitly. The proposed solution gives exact concurrence with accessible literature.