Vertical vibration of a rigid disc over a transversely isotropic and layered poroelastic half-space

A novel semi-analytical method is proposed for solving the vertical vibration of a rigid disc over a transversely isotropic and layered poroelastic half-space. The fundamental solutions in the layered poroelastic half-space under a vertical patch load on the surface are solved in terms of the newly developed Fourier-Bessel series (FBS) system of vector functions and the unconditionally stable dual-variable and position method. The expansion coefficients in FBS system are discrete, as such the computational efficiency is greatly improved and the accuracy is better than the commonly used integral-transform methods. By virtue of the superposition method, the Green's function due to vertical ring load is derived in the transform domain. By making use of the integral least-square scheme, the densities of a series of ring loads discretized within the disc area are determined. Finally, the dynamic vertical compliance is derived via the balance between the external applied force and the induced total contact traction. After verifying the reliability of the developed solution, selected numerical examples are presented to investigate the influence of material properties and excitation frequency on the forced vibration of the rigid disc.