In this study, the plane wave finite element (PWFE) method for the 2-D phononic crystal (PC) under elastic waves is proposed. The 2-D PC is supposed to be infinite in the horizontal directions and finite in the vertical and the PC layer is sandwiched between two half-spaces. To establish the PWFE model, the plane wave expansion is performed along the horizontal direction of the PC first, and the virtual work principle for each plane wave is then derived. By using the virtual work principle for the plane wave, and implementing the conventional finite element procedure, the FE equations for each plane wave are established. Assembling the FE equations for all plane waves yields the FE equations for the 2D PC. The traction-displacement relations on the surfaces of the lower and upper half-spaces are derived and used to impose the transmitting boundary conditions at the top and bottom of the PC layer. Synthesizing the contributions from all plane waves via the DFT method, the dynamic response of the PC layer to the incident wave is determined. To validate the proposed FEM model, results due to the proposed model are compared with those due to the transfer matrix method and existing results. The numerical results of this study show that the frequency domain response of the PC layer to elastic waves has remarkable resonance nature. The locations of resonance peaks are different for the elastic waves with different incident angles, and also are different for the PC layer with different filling fractions.
展开▼
