Dynamic response of a multi-layer elastic medium subjected to harmonic surface concentrated load is considered. In development of the analytical solution, the three-dimensional theory of elasto-dynamic is utilized for derivation of the governing partial differential equations for each layer. These equations are solved in the Fourier domain by employing the Double Complex Fourier Transform technique. In the analysis, each layer of the medium is assumed to be extended infinitely in the horizontal x and z directions and has uniform depth in the y direction and is considered to be linearly elastic, homogeneous, and isotropic. Utilizing the Integral Fourier Transform, displacements and stresses at any point in each layer can be determined in terms of boundary stresses for each layer. Also, the presented solution provides the relation between stress and displacement vectors for the top and bottom of each layer in matrix notation. By satisfying the compatibility of displacements and stresses for each interface, a propagator matrix relating displacements and stresses at the top of the medium to the bottom interface will be obtained. This relates the displacement and stress vector on the top surface to the bottom interface by eliminating similar information for the other interfaces. In this study, the displacements on the surface of the layered medium are computed for the two cases where the surface of the medium is subjected to a concentrated harmonic vertical or horizontal harmonic force.

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