A meshfree local RBF collocation method for anti-plane transverse elastic wave propagation analysis in 2D phononic crystals

作者：Zheng, Hui; Zhang, Chuanzeng^*; Wang, Yuesheng; Sladek, Jan; Sladek, Vladimir

来源：Journal of Computational Physics, 2016, 305: 997-1014.

DOI：10.1016/j.jcp.2015.10.020

• Local RBF collocation method
• Meshfree or meshless method
• Two-dimensional phononic crystals
• Band structures
• Anti-plane transverse elastic waves

In this paper, a meshfree or meshless local radial basis RBF) collocation method is proposed to calculate the band structures of two-dimensional (2D) anti-plane transverse elastic waves in phononic crystals. Three new techniques are developed for calculating the normal derivative of the field quantity required by the treatment of the boundary conditions, which improve the stability of the local RBF collocation method significantly. The general form of the local RBF collocation method for a unit-cell with periodic boundary conditions is proposed, where the continuity conditions on the interface between the matrix and the scatterer are taken into account. The band structures or dispersion relations can be obtained by solving the eigenvalue problem and sweeping the boundary of the irreducible first Brillouin zone. The proposed local RBF collocation method is verified by using the corresponding results obtained with the finite element method. For different acoustic impedance ratios, various scatterer shapes, scatterer arrangements (lattice forms) and material properties, numerical examples are presented and discussed to show the performance and the efficiency of the developed local RBF collocation method compared to the FEM for computing the band structures of 2D phononic crystals.

• 出版日期2016-1-15
• 单位北京交通大学; 中国地震局工程力学研究所