Dynamic response of the multilayered half-space medium due to the spatially periodic harmonic moving load

Abstract

This study theoretically investigated the dynamic responses of a multilayered half-space subjected to a spatially periodic harmonic moving load using the direct stiffness method. First, a periodic model of the multilayered half-space was established. Based on the generalised modal functions and Fourier transform, the direct stiffness matrices relating displacements and tractions along layer interfaces for both the interior layers and semi-infinite region were derived. A global direct stiffness matrix was established by assembling the direct stiffness matrix for each layer. Then, the accuracy and feasibility of the proposed direct stiffness method were verified by comparing the results in the homogeneous and multilayered half-spaces with the literature. Finally, parametric analyses were conducted to investigate the effects of wavenumber in one periodicity length, ground layering, load speed, and load frequency on the dynamic responses. It is concluded that the characteristics of the displacement responses in the horizontal direction differ from those in the vertical direction in both time and frequency domains. The increase in wavenumber, load speed, and load frequency decreased the response amplitudes, increased the characteristic frequencies, and broadened the critical frequency bandwidths. The increase in the layer number broadens the critical frequency bandwidths, but it has no impact on the characteristic frequencies. The moving and Doppler effects cause variations in the characteristic frequencies and critical frequency bandwidths. The results of the multilayered half-space under spatially periodic harmonic moving load can be utilised as fundamental solutions in the periodic boundary element formulations, which will be the focus of future work.