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

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

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 o...

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Main Authors: Lin Han, Yan Zhang, Xiao-mei Li, Lin-hua Jiang, Da Chen
Format: Article
Language:English
Published: MDPI AG 2016-01-01
Series:Crystals
Subjects:
phononic crystal
band structure
finite element method
mass matrix
weighting treatment
convergence speed
Online Access:http://www.mdpi.com/2073-4352/6/1/11
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spelling doaj-57fa9d64c29246a68c676dbc1ab2a9712020-11-25T00:34:21ZengMDPI AGCrystals2073-43522016-01-01611110.3390/cryst6010011cryst6010011Accelerated Approach for the Band Structures Calculation of Phononic Crystals by Finite Element MethodLin Han0Yan Zhang1Xiao-mei Li2Lin-hua Jiang3Da Chen4College of Mechanics and Materials, Hohai University, Nanjing 210098, ChinaCollege of Mechanics and Materials, Hohai University, Nanjing 210098, ChinaCollege of Civil Engineering, Tongji University, Shanghai 200092, ChinaCollege of Mechanics and Materials, Hohai University, Nanjing 210098, ChinaCollege of Harbour, Coastal and Offshore Engineering, Hohai University, Nanjing 210098, ChinaWe 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.http://www.mdpi.com/2073-4352/6/1/11phononic crystalband structurefinite element methodmass matrixweighting treatmentconvergence speed
collection DOAJ
language English
format Article
sources DOAJ
author Lin Han
Yan Zhang
Xiao-mei Li
Lin-hua Jiang
Da Chen
spellingShingle Lin Han
Yan Zhang
Xiao-mei Li
Lin-hua Jiang
Da Chen
Accelerated Approach for the Band Structures Calculation of Phononic Crystals by Finite Element Method
Crystals
phononic crystal
band structure
finite element method
mass matrix
weighting treatment
convergence speed
author_facet Lin Han
Yan Zhang
Xiao-mei Li
Lin-hua Jiang
Da Chen
author_sort Lin Han
title Accelerated Approach for the Band Structures Calculation of Phononic Crystals by Finite Element Method
title_short Accelerated Approach for the Band Structures Calculation of Phononic Crystals by Finite Element Method
title_full Accelerated Approach for the Band Structures Calculation of Phononic Crystals by Finite Element Method
title_fullStr Accelerated Approach for the Band Structures Calculation of Phononic Crystals by Finite Element Method
title_full_unstemmed Accelerated Approach for the Band Structures Calculation of Phononic Crystals by Finite Element Method
title_sort accelerated approach for the band structures calculation of phononic crystals by finite element method
publisher MDPI AG
series Crystals
issn 2073-4352
publishDate 2016-01-01
description 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.
topic phononic crystal
band structure
finite element method
mass matrix
weighting treatment
convergence speed
url http://www.mdpi.com/2073-4352/6/1/11
work_keys_str_mv AT linhan acceleratedapproachforthebandstructurescalculationofphononiccrystalsbyfiniteelementmethod
AT yanzhang acceleratedapproachforthebandstructurescalculationofphononiccrystalsbyfiniteelementmethod
AT xiaomeili acceleratedapproachforthebandstructurescalculationofphononiccrystalsbyfiniteelementmethod
AT linhuajiang acceleratedapproachforthebandstructurescalculationofphononiccrystalsbyfiniteelementmethod
AT dachen acceleratedapproachforthebandstructurescalculationofphononiccrystalsbyfiniteelementmethod
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