Dynamic Response of Ground Surface Due to External Disturbance: Analytical Solution

In this investigation the propagation of a harmonic disturbance on the surface of ground is considered. The medium is assumed to be a homogeneous and isotropic, continuous and infinite which can be modeled as an elastic half space medium. Implementing elasto-dynamics analysis, the governing equation of motion for the system is developed. The developed mathematical model formulates the displacement and stresses in the medium in terms of elastic dilatation and rotations and reduces the governing equations into three wave equations in terms of elastic dilatation and rotations. These equations are solved and boundary stresses are satisfied in Fourier domain and the displacement on the surface are provided in this domain.