TY - JOUR

T1 - A localized meshless collocation method for bandgap calculation of anti-plane waves in 2D solid phononic crystals

AU - Fu, Zhuo Jia

AU - Li, Ai Lun

AU - Zhang, Chuanzeng

AU - Fan, Chia Ming

AU - Zhuang, Xiao Ying

N1 - 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 ) .

PY - 2020/10

Y1 - 2020/10

N2 - 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.

AB - 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.

KW - 2D solid phononic crystal

KW - Anti-plane elastic wave

KW - Generalized finite difference method

KW - Meshless collocation method

KW - Moving least square method

KW - Taylor series expansion

UR - http://www.scopus.com/inward/record.url?scp=85088369120&partnerID=8YFLogxK

U2 - 10.1016/j.enganabound.2020.07.014

DO - 10.1016/j.enganabound.2020.07.014

M3 - Article

AN - SCOPUS:85088369120

VL - 119

SP - 162

EP - 182

JO - Engineering Analysis with Boundary Elements

JF - Engineering Analysis with Boundary Elements

SN - 0955-7997

ER -