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 引用本文: 徐杰, 郑辉, 石承志, 闫雪豹, 文丕华. 含裂纹声子晶体能带分析的改进局部径向基函数配点法. 力学学报, 待出版.
Xu Jie, Zheng Hui, Shi Chengzhi, Yan Xuebao, Wen Pihua. Improved local radial basis function collocation method for band structure analysis of cracked phononic crystals. Chinese Journal of Theoretical and Applied Mechanics, in press.
 Citation: Xu Jie, Zheng Hui, Shi Chengzhi, Yan Xuebao, Wen Pihua. Improved local radial basis function collocation method for band structure analysis of cracked phononic crystals. Chinese Journal of Theoretical and Applied Mechanics, in press.

## IMPROVED LOCAL RADIAL BASIS FUNCTION COLLOCATION METHOD FOR BAND STRUCTURE ANALYSIS OF CRACKED PHONONIC CRYSTALS

• 摘要: 基于直接法局部径向基函数配点法(local radial basis function collocation method, LRBFCM)提出了含裂纹声子晶体反平面弹性波的能带结构计算方法, 分析了其能带结构特性, 并通过有限元法计算对比验证该数值结果的准确性和有效性. 在边界上采用直接法沿方向取局部节点, 解决了边界求解不稳定问题, 讨论了数值方法的处理技巧对结果的影响. 并通过考虑不同声阻抗比、散射体形状(方形、圆形)和裂纹情况, 验证了该方法计算含裂纹声子晶体能带结构的适用性. 研究了形状参数、配点数对计算结果的影响. 最后深入分析了不同长度和位置的裂纹对声子晶体能带结构的影响特性, 并进行了对比分析. 文章的创新性在于用直接法局部径向基函数配点法解决了含裂纹声子晶体能带结构计算的问题, 极大增加了声子晶体的应用价值. 研究结果显示: 随着裂纹的扩展, 能带结构带隙逐渐变窄; 当裂纹扩展到一定程度时, 金散射体的声子晶体带隙数量会增加, 且新增带隙会随着裂纹扩展而变宽, 但铝散射体的声子晶体带隙数量会减少; 直接法局部径向基函数配点法可以大大提高含裂纹声子晶体能带结构的计算效率和计算精度.

Abstract: Based on the direct local radial basis function collocation method (LRBFCM), the energy band structure calculation algorithm for the anti-plane elastic wave of the cracked phononic crystals is proposed. The energy band structure characteristics are analyzed, and the accuracy and validity of the numerical results are verified with the comparison of the finite element method analysis. For the boundary collocation nodes, the direct method is adopted to select local nodes along the normal direction to solve the problems of stability, and the influence of the processing techniques of the numerical methods on the results is discussed. The applicability of the method for calculating the energy band structure of cracked phononic crystals is verified by considering different acoustic impedance ratios, scatterer shapes (square, circular) and crack conditions. The effects of shape parameters and the number of point numbers on the calculation results are investigated. Finally, the effects of crack of different length and its location on the energy band structure of phononic crystals are analyzed comprehensively, and a comparative analysis is carried out. The innovation of this paper is to solve the problem of calculating the energy band structure of cracked phononic crystals by the direct method of local radial basis function collocation method, which greatly increases the application value of phononic crystals. The results in this work show that due to the crack propagation, the bandgap of the phononic crystals structure gradually narrows; When the crack expands to a certain extent, the number of bandgaps in the phononic crystals of aurum scatterers increases, and the new bandgaps widen with the expansion of the crack. However, the number of bandgaps in the phononic crystals of aluminum scatterers decreases; The direct local radial basis function collocation method can improve the calculation efficiency and the computational accuracy significantly for the energy band structure of cracked phononic crystals.

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