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Applied Mathematics and Mechanics

, Volume 37, Issue 5, pp 627–638 | Cite as

RBF collocation method and stability analysis for phononic crystals

  • Chunqiu Wei
  • Zhizhong YanEmail author
  • Hui Zheng
  • Chuanzeng Zhang
Article

Abstract

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.

Key words

radial basis function (RBF) phononic crystal (PC) stability 

Chinese Library Classification

O29 O34 

2010 Mathematics Subject Classification

65M70 

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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Chunqiu Wei
    • 1
    • 2
  • Zhizhong Yan
    • 1
    • 2
    Email author
  • Hui Zheng
    • 3
  • Chuanzeng Zhang
    • 3
  1. 1.School of Mathematics and StatisticsBeijing Institute of TechnologyBeijingChina
  2. 2.Beijing Key Laboratory on MCAACIBeijing Institute of TechnologyBeijingChina
  3. 3.Department of Civil EngineeringUniversity of SiegenSiegenGermany

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