Forced vibration of surface foundation on multi-layered half space

A numerical approach is presented for the analysis of the forced vibration of a rigid surface foundation with arbitrary shape. In the analysis, the foundation is discretized into a number of sub square-elements. The dynamic response within each sub-element is described by the Green's function, which is obtained by the Fourier-Bessel transform and Precise Integration Method (PIM). Incorporating the displacement boundary condition and force equilibrium of the foundation, it obtains a system of linear algebraic equation in terms of the contact forces within each sub-element. Solving the equation leads to the desired dynamic impedance functions of the foundation. Numerical results are obtained for foundation not only with simple geometrical configurations, such as rectangular and circular foundation, but also the case of irregularly shaped foundation. Several comparisons between the proposed approach and other methods are made. Very good agreement is reached. Also, parametric studies are carried out on the dynamic response of foundation. Addressed in this study are the effects of Poisson's ratio, material damping and contact condition of soil-foundation interface. Several conclusions are drawn the significance of the factors.