Vertical vibration of a massless flexible strip footing bonded to a transversely isotropic multilayered half-plane

A rigorous analytical method is developed to analyze the vertical vibration of a massless flexible strip footing bonded to a transversely isotropic multilayered half-plane. The analytical layer-element solution for a transversely isotropic multilayered half-plane in the Fourier transform domain is first introduced for the later derivation. A pair of dual integral equations of contact stress and deflection is derived by virtue of the preceding solution and the mixed boundary conditions. By means of the classic plate theory and Jacobi orthogonal polynomials, the dual integral equations are further converted to a system of linear equations. Comparisons with existed solutions confirm the accuracy of the proposed method. More examples are given to illustrate the influence of relative rigidity ratio, transversely isotropy, double-layered characters and stratification on the vertical impedance and the contact stress.