A Meshless Weak-form RBF Method for Calculating the Elastic Wave Band Structures of Layered Phononic Crystals

In this paper, a meshless local weak-form method based on compact radial basis functions (RBFs) is proposed to calculate the band structures of layered phononic crystals. The displacement function is represented by a set of radial basis functions, and the general form of the proposed RBF method for a unit-cell is derived by using the variational principle with consideration of the periodic boundary conditions. The band structures can be obtained by solving a matrix eigenvalue problem. The novel weak-form RBF method is verified by the finite element method (FEM). For different acoustic impedance ratios and length ratios, numerical examples are presented and discussed to show the efficiency of the proposed weak-form RBF method compared to the FEM and the strong-form RBF method for calculating the band structures of layered phononic crystals.