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RBF collocation method and stability analysis for phononic crystals

ISSN号：0253-4827
期刊名称：《应用数学和力学：英文版》
时间：0
分类：TP183[自动化与计算机技术—控制科学与工程;自动化与计算机技术—控制理论与控制工程] TS943.11[轻工技术与工程—服装设计与工程]
作者机构：[1]School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China, [2]Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing 100081, China, [3]Department of Civil Engineering, University of Siegen, Siegen D-57076, Germany
相关基金：Project support by the National Natural Science Foundation of China （Nos. 11002026 and 11372039）, the Beijing Natural Science Foundation （No. 3133039）, and the Scientific Research Foundation for the Returned Overseas Chinese Scholars （No. 20121832001）

作者： Chunqiu WEI[1,2], Zhizhong YAN[1,2], Hui ZHENG[3], Chuanzeng ZHANG[3]

关键词：稳定性分析, 搭配方法, RBF, 声子晶体, 径向基函数, 周期结构, 能带结构, 复合结构, radial basis function （RBF）, phononic crystal （PC）, stability

中文摘要：

The mesh-free radial basis function(RBF) collocation method is explored to calculate band structures of periodic composite structures. The inverse multi-quadric(MQ), Gaussian, and MQ RBFs are used to test the stability of the RBF collocation method in periodic structures. Much useful information is obtained. Due to the merits of the RBF collocation method, the general form in this paper can easily be applied in the high dimensional problems analysis. The stability is fully discussed with different RBFs.The choice of the shape parameter and the effects of the knot number are presented.

英文摘要：

The mesh-free radial basis function （RBF） collocation method is explored to calculate band structures of periodic composite structures. The inverse multi-quadric （MQ）, Gaussian, and MQ RBFs are used to test the stability of the RBF collocation method in periodic structures. Much useful information is obtained. Due to the merits of the RBF collocation method, the general form in this paper can easily be applied in the high dimensional problems analysis. The stability is fully discussed with different RBFs. The choice of the shape parameter and the effects of the knot number are presented.

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