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Open AccessArticle

Band Structures Analysis Method of Two-Dimensional Phononic Crystals Using Wavelet-Based Elements

by Mao Liu 1,2, Jiawei Xiang 1,* and Yongteng Zhong 1
1
College of Mechanical and Electrical Engineering, Wenzhou University, Wenzhou 325035, China
2
Division of Dynamics and Control, School of Astronautics, Harbin Institute of Technology, Harbin 150001, China
*
Author to whom correspondence should be addressed.
Academic Editors: Abdelkrim Khelif and Sarah Benchabane
Crystals 2017, 7(11), 328; https://doi.org/10.3390/cryst7110328
Received: 12 September 2017 / Revised: 17 October 2017 / Accepted: 27 October 2017 / Published: 31 October 2017
(This article belongs to the Special Issue Phononics)
A wavelet-based finite element method (WFEM) is developed to calculate the elastic band structures of two-dimensional phononic crystals (2DPCs), which are composed of square lattices of solid cuboids in a solid matrix. In a unit cell, a new model of band-gap calculation of 2DPCs is constructed using plane elastomechanical elements based on a B-spline wavelet on the interval (BSWI). Substituting the periodic boundary conditions (BCs) and interface conditions, a linear eigenvalue problem dependent on the Bloch wave vector is derived. Numerical examples show that the proposed method performs well for band structure problems when compared with those calculated by traditional FEM. This study also illustrates that filling fractions, material parameters, and incline angles of a 2DPC structure can cause band-gap width and location changes. View Full-Text
Keywords: wavelet finite element method; band-gaps; phononic crystals; B-spline wavelet on the interval wavelet finite element method; band-gaps; phononic crystals; B-spline wavelet on the interval
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MDPI and ACS Style

Liu, M.; Xiang, J.; Zhong, Y. Band Structures Analysis Method of Two-Dimensional Phononic Crystals Using Wavelet-Based Elements. Crystals 2017, 7, 328.

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