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Crystals 2016, 6(1), 11; doi:10.3390/cryst6010011

Accelerated Approach for the Band Structures Calculation of Phononic Crystals by Finite Element Method

1
College of Mechanics and Materials, Hohai University, Nanjing 210098, China
2
College of Civil Engineering, Tongji University, Shanghai 200092, China
3
College of Harbour, Coastal and Offshore Engineering, Hohai University, Nanjing 210098, China
*
Author to whom correspondence should be addressed.
Academic Editors: Victor J. Sanchez-Morcillo, Vicent Romero-Garcia and Luis M. Garcia-Raffi
Received: 22 December 2015 / Revised: 11 January 2016 / Accepted: 12 January 2016 / Published: 14 January 2016
(This article belongs to the Special Issue Phononic Crystals)
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Abstract

We present here a fast and easily realized computational approach based on the finite element methods with consistent and lumped mass matrices (CM-FEM and LM-FEM, respectively), and the Bloch’s theorem, to calculate the elastic band structures of phononic crystals. Two improvements, the adjustment of the introduction of Bloch’s theorem as well as weighting treatment of consistent and lumped mass matrices, are performed. Numerical simulations show that convergence speed is accelerated obviously. Furthermore, the method is verified by analytical solutions in specified homogeneous cases. It is concluded that compared with CM-FEM or LM-FEM, the present method gives higher precision results with sparser mesh and takes less time. View Full-Text
Keywords: phononic crystal; band structure; finite element method; mass matrix; weighting treatment; convergence speed phononic crystal; band structure; finite element method; mass matrix; weighting treatment; convergence speed
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Han, L.; Zhang, Y.; Li, X.-M.; Jiang, L.-H.; Chen, D. Accelerated Approach for the Band Structures Calculation of Phononic Crystals by Finite Element Method. Crystals 2016, 6, 11.

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