Plane Wave Finite Element Method for the Dynamic Response of the Periodic Pile-Type Composite Ground Under a Harmonic Concentrated Load

Abstract

In this study, a simplified model for the pile-type composite ground, namely, the periodic pile-type composite ground (PPCG) model is proposed. The PPCG in this study is assumed to be periodic in the horizontal directions and finite in the vertical direction. For investigation of the dynamic response of the PPCG to a harmonic concentrated load, a plane wave finite element (PWFE) method for the PPCG under the load is developed in this study. To develop the method, the concentrated load is decomposed into its wavenumber domain components by the 2D Fourier transform first. The response of the PPCG to a wavenumber domain load component is represented by a set of plane waves, and the variables associated with each plane wave are discretized via the FEM along the vertical direction of the PPCG. The finite element equations for each plane wave of the PPCG are developed via the virtual work principle. To obtain the overall dynamic response of the PPCG to the concentrated load by synthesizing the responses due to all load components effectively, the mode superposition method is used to construct the response of the PPCG to the load component, and the polar coordinate system-based inverse Fourier transform method is developed for the inversion of the 2D Fourier transform with respect to the wavenumber. With the developed method, some numerical results about the dynamic response of the PPCG to the concentrated load are presented.