Vertical vibration of a rigid strip footing on a transversely isotropic multilayered half-plane

A rigorous analytical method is developed to analyze the vertical vibration of a rigid strip footing on a transversely isotropic multilayered half-plane. Based on mixed boundary conditions for the interaction problem and the analytical layer-element solution for the multilayered half-plane, a pair of dual integral equations of contact stress is derived in the Fourier transform domain. By means of Jacobi orthogonal polynomials, the dual integral equations are converted to a system of linear equations and further solved. Fourier inverse transform is carried out to obtain the final results in the frequency domain. Comparisons with the existing solutions confirm the accuracy of the proposed method and more examples are given to illustrate the influence of material anisotropy and stratification.