Band structure computation of in-plane elastic waves in 2D phononic crystals by a meshfree local RBF collocation method

Hui Zheng, Zhang Chuanzeng, Yuesheng Wang, Jan Sladek, Vladimir Sladek

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

In this paper, the band structures of in-plane elastic waves in two-dimensional (2D) phononic crystals are calculated by using a meshfree local radial basis functions (RBF) collocation method. In order to improve the stability of the local RBF collocation method, special techniques suggested in our previous work for anti-plane waves are further improved and extended for calculating the primary field quantities and their normal derivatives required by the treatment of the boundary conditions in the local RBF collocation method for computing the band structures of the in-plane elastic waves in 2D phononic crystals. The developed meshfree local RBF collocation method for the band structure calculations of in-plane elastic waves propagating in 2D phononic crystals is validated by using the corresponding numerical results obtained with the finite element method (FEM). The band structures of different material combinations or acoustic impedance ratios, different filling fractions, various lattice forms and scatterer shapes are computed numerically to show the accuracy and the efficiency of the meshfree local RBF collocation method for computing the band structures of in-plane elastic waves in 2D phononic crystals.
Original languageEnglish
Pages (from-to)77-90
Number of pages14
JournalEngineering Analysis with Boundary Elements
Volume66
DOIs
Publication statusPublished - 15 May 2016
Externally publishedYes

Fingerprint

collocation
elastic waves
crystals
acoustic impedance
finite element method
plane waves
impedance
boundary conditions
scattering

Keywords

  • Elastic waves
  • 2D phononic crystals
  • Band structures
  • Band gaps
  • Eigenvalue problems
  • Radial basis functions
  • Collocation method
  • Finite element method

Cite this

Band structure computation of in-plane elastic waves in 2D phononic crystals by a meshfree local RBF collocation method. / Zheng, Hui; Chuanzeng, Zhang; Wang, Yuesheng; Sladek, Jan; Sladek, Vladimir.

In: Engineering Analysis with Boundary Elements, Vol. 66, 15.05.2016, p. 77-90.

Research output: Contribution to journalArticle

Zheng, Hui ; Chuanzeng, Zhang ; Wang, Yuesheng ; Sladek, Jan ; Sladek, Vladimir. / Band structure computation of in-plane elastic waves in 2D phononic crystals by a meshfree local RBF collocation method. In: Engineering Analysis with Boundary Elements. 2016 ; Vol. 66. pp. 77-90.
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abstract = "In this paper, the band structures of in-plane elastic waves in two-dimensional (2D) phononic crystals are calculated by using a meshfree local radial basis functions (RBF) collocation method. In order to improve the stability of the local RBF collocation method, special techniques suggested in our previous work for anti-plane waves are further improved and extended for calculating the primary field quantities and their normal derivatives required by the treatment of the boundary conditions in the local RBF collocation method for computing the band structures of the in-plane elastic waves in 2D phononic crystals. The developed meshfree local RBF collocation method for the band structure calculations of in-plane elastic waves propagating in 2D phononic crystals is validated by using the corresponding numerical results obtained with the finite element method (FEM). The band structures of different material combinations or acoustic impedance ratios, different filling fractions, various lattice forms and scatterer shapes are computed numerically to show the accuracy and the efficiency of the meshfree local RBF collocation method for computing the band structures of in-plane elastic waves in 2D phononic crystals.",
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AU - Chuanzeng, Zhang

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AU - Sladek, Jan

AU - Sladek, Vladimir

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N2 - In this paper, the band structures of in-plane elastic waves in two-dimensional (2D) phononic crystals are calculated by using a meshfree local radial basis functions (RBF) collocation method. In order to improve the stability of the local RBF collocation method, special techniques suggested in our previous work for anti-plane waves are further improved and extended for calculating the primary field quantities and their normal derivatives required by the treatment of the boundary conditions in the local RBF collocation method for computing the band structures of the in-plane elastic waves in 2D phononic crystals. The developed meshfree local RBF collocation method for the band structure calculations of in-plane elastic waves propagating in 2D phononic crystals is validated by using the corresponding numerical results obtained with the finite element method (FEM). The band structures of different material combinations or acoustic impedance ratios, different filling fractions, various lattice forms and scatterer shapes are computed numerically to show the accuracy and the efficiency of the meshfree local RBF collocation method for computing the band structures of in-plane elastic waves in 2D phononic crystals.

AB - In this paper, the band structures of in-plane elastic waves in two-dimensional (2D) phononic crystals are calculated by using a meshfree local radial basis functions (RBF) collocation method. In order to improve the stability of the local RBF collocation method, special techniques suggested in our previous work for anti-plane waves are further improved and extended for calculating the primary field quantities and their normal derivatives required by the treatment of the boundary conditions in the local RBF collocation method for computing the band structures of the in-plane elastic waves in 2D phononic crystals. The developed meshfree local RBF collocation method for the band structure calculations of in-plane elastic waves propagating in 2D phononic crystals is validated by using the corresponding numerical results obtained with the finite element method (FEM). The band structures of different material combinations or acoustic impedance ratios, different filling fractions, various lattice forms and scatterer shapes are computed numerically to show the accuracy and the efficiency of the meshfree local RBF collocation method for computing the band structures of in-plane elastic waves in 2D phononic crystals.

KW - Elastic waves

KW - 2D phononic crystals

KW - Band structures

KW - Band gaps

KW - Eigenvalue problems

KW - Radial basis functions

KW - Collocation method

KW - Finite element method

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DO - 10.1016/j.enganabound.2016.01.012

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