A localized meshless collocation method for bandgap calculation of anti-plane waves in 2D solid phononic crystals

authored by: Zhuo Jia Fu, Ai Lun Li, Chuanzeng Zhang, Chia Ming Fan, Xiao Ying Zhuang
Abstract: In this paper, a localized meshless collocation method, the generalized finite difference method (GFDM), is first applied to calculate the bandgaps of anti-plane transverse elastic waves in 2D solid phononic crystals with square and triangular lattice. The corresponding theoretical consistency analysis of the GFDM is given. The universal algorithm for the uniform/scattered node generation in the GFDM is presented. In comparison with the traditional plane wave expansion (PWE) method and Pressure Acoustics Module in COMSOL software, the proposed GFDM can provide the similar accurate results with less computational times for calculating the band structures of the simple/complicated shape scatterers in the square/triangular lattice. Three influence factors (Filling fractions (Ff), rotation angles (Ra) and arm widths (Aw) in the unit-cell) of the bandgap properties in 2D phononic crystals are numerically discussed.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Hohai University
Nanjing University of Aeronautics and Astronautics
University of Siegen
National Taiwan Ocean University
Type: Article
Journal: Engineering Analysis with Boundary Elements
Volume: 119
Pages: 162-182
No. of pages: 21
ISSN: 0955-7997
Publication date: 10.2020
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Analysis, General Engineering, Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1016/j.enganabound.2020.07.014 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{139f35fde0a34d18bfbfb90bc2d1089e,
title = "A localized meshless collocation method for bandgap calculation of anti-plane waves in 2D solid phononic crystals",
abstract = "In this paper, a localized meshless collocation method, the generalized finite difference method (GFDM), is first applied to calculate the bandgaps of anti-plane transverse elastic waves in 2D solid phononic crystals with square and triangular lattice. The corresponding theoretical consistency analysis of the GFDM is given. The universal algorithm for the uniform/scattered node generation in the GFDM is presented. In comparison with the traditional plane wave expansion (PWE) method and Pressure Acoustics Module in COMSOL software, the proposed GFDM can provide the similar accurate results with less computational times for calculating the band structures of the simple/complicated shape scatterers in the square/triangular lattice. Three influence factors (Filling fractions (Ff), rotation angles (Ra) and arm widths (Aw) in the unit-cell) of the bandgap properties in 2D phononic crystals are numerically discussed.",
keywords = "2D solid phononic crystal, Anti-plane elastic wave, Generalized finite difference method, Meshless collocation method, Moving least square method, Taylor series expansion",
author = "Fu, {Zhuo Jia} and Li, {Ai Lun} and Chuanzeng Zhang and Fan, {Chia Ming} and Zhuang, {Xiao Ying}",
note = "Funding Information: The authors thank the anonymous reviewers of this article for their very helpful comments and suggestions to significantly improve the academic quality of this article. The work described in this paper was supported by the National Science Fund of China (Grant No. 11772119 ), the Foundation for Open Project of State Key Laboratory of Mechanics and Control of Mechanical Structures ( Nanjing University Of Aeronautics And Astronautics ) (Grant No. MCMS-E-0519G01 ), the Foundation for Open Project of Key Laboratory of Coastal Disaster and Defence of Ministry of Education (Grant No. 201907 ), Alexander von Humboldt Research Fellowship (ID: 1195938 ) and the Six Talent Peaks Project in Jiangsu Province of China (Grant No. 2019-KTHY-009 ) . ",
year = "2020",
month = oct,
doi = "10.1016/j.enganabound.2020.07.014",
language = "English",
volume = "119",
pages = "162--182",
journal = "Engineering Analysis with Boundary Elements",
issn = "0955-7997",
publisher = "Elsevier Ltd.",
}