A meshless collocation method for band structure simulation of nanoscale phononic crystals based on nonlocal elasticity theory

•A meshfree LRBFCM based on the nonlocal elasticity theory is developed for wave propagation analysis in nanoscale phononic crystals.•The band structures of 1D nanoscale phononic crystals obtained by the LRBFCM agree well with the reference results.•The band structures and transmission coefficients...

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Bibliographic Details
Published in:Journal of computational physics Vol. 408; p. 109268
Main Authors: Zheng, Hui, Zhou, Chuanbing, Yan, Dong-Jia, Wang, Yue-Sheng, Zhang, Chuanzeng
Format: Journal Article
Language:English
Published: Cambridge Elsevier Inc 01.05.2020
Elsevier Science Ltd
Subjects:
Band structure of solids
Band structures
Collocation methods
Computational physics
Crystal structure
Elastic waves
First principles
Mathematical analysis
Meshless methods
Nanoscale phononic crystals
Nonlocal elasticity
Nonlocal elasticity theory
Periodic structures
Radial basis function
Radial basis functions
Transfer matrices
Band structures
Nanoscale phononic crystals
Radial basis functions
Elastic waves
Nonlocal elasticity theory
ISSN:0021-9991, 1090-2716
Online Access:Get full text
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Summary:•A meshfree LRBFCM based on the nonlocal elasticity theory is developed for wave propagation analysis in nanoscale phononic crystals.•The band structures of 1D nanoscale phononic crystals obtained by the LRBFCM agree well with the reference results.•The band structures and transmission coefficients of elastic waves in 2D nanoscale phononic crystals are computed and analyzed by the LRBFCM. In this paper, the band structures of nanoscale phononic crystals based on the nonlocal elasticity theory are calculated by using a meshfree local radial basis function collocation method (LRBFCM). The direct method is applied to enhance the stability of the derivative calculations in the LRBFCM. A simple summation in the LRBFCM is proposed to deal with the integration related to the nonlocal stresses or tractions. The LRBFCM for the band structure calculations is validated by the results obtained with the first-principle and the transfer matrix (TM) method for one-dimensional (1D) phononic crystals, as well as the comparison of the frequency responses of the two-dimensional (2D) periodic structures.
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ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2020.109268