A Chebyshev collocation method for band structure calculations of the longitudinal elastic waves in phononic crystals

Abstract

AbstractIn this study, a Chebyshev collocation method (CCM) is developed and applied to calculate the band structures of longitudinal elastic waves in periodically multi‐layered phononic crystals. The general form of the CCM for a unit‐cell is derived, in which the periodic boundary conditions and continuity conditions on the interface between different component materials are imposed directly to the CCM scheme. The band structures or dispersion relations can be obtained by solving the corresponding linear eigenvalue problem, where the unknown frequencies are the eigenvalues and the components of the Bloch wave vector are given. The proposed CCM is verified by using the corresponding results obtained by the transfer matrix method. Due to the advantages of the CCM, the CCM presented in this paper can be easily generalized and applied to the high‐dimensional such as two‐dimensional (2D) problems.