Investigation of finite/infinite unidirectional elastic phononic plates by BEM

Abstract

The investigation of finite/infinite unidirectional elastic phononic plates is carried out by using the boundary element method (BEM). The transmissions of elastic waves in finite structures are calculated by solving a size-reduced system matrix, in which the transfer matrix formulated by BEM is used repeatedly and the unknown quantities on the free boundaries of cells are removed. For the infinite structures, the Bloch theorem is applied to the unit cell that has traction free boundaries, and the dispersion relation is plotted by extracting the eigenfrequencies of the nonlinear Bloch eigenvalue problem using a contour integral method. Furthermore, the eigenfrequencies of the finite structure are extracted by applying the contour integral method to the sized reduced system matrix, and a banded distribution of the eigenfrequencies is found. The correlation between the band structures of the infinite structures and the elastic wave transmission of the corresponding finite structures are presented. The frequency-banded nature exhibited by the finite structures shows a good agreement with the band structure of the corresponding infinite structures.