An exact solution to compute the band gap in phononic crystals

Eric Li; Z. C. He; Gao Wang

doi:10.1016/j.commatsci.2016.05.004

An exact solution to compute the band gap in phononic crystals

Eric Li, Z. C. He, Gao Wang

SCEDT Engineering

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

In this paper, an alpha finite element method (αFEM) is formulated to study the propagation of elastic waves in periodic crystals. Using the simple triangular elements, the αFEM with optimal α value can always provide the exact solutions in the prediction of the band gap of phononic crystals. In addition, the upper and lower solutions are always observed in the computation of the band gap of phononic crystals with the adjustment of α value. The performance of αFEM is compared with standard finite element method (FEM) with different types of mass matrix formulation. The numerical examples have strongly demonstrated that the αFEM has given more accuracy prediction in the analysis of phononic crystals compared with standard FEM.

Original language	English
Pages (from-to)	72-85
Number of pages	14
Journal	Computational Materials Science
Volume	122
DOIs	https://doi.org/10.1016/j.commatsci.2016.05.004
Publication status	Published - 1 Sept 2016

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10.1016/j.commatsci.2016.05.004

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title = "An exact solution to compute the band gap in phononic crystals",

abstract = "In this paper, an alpha finite element method (αFEM) is formulated to study the propagation of elastic waves in periodic crystals. Using the simple triangular elements, the αFEM with optimal α value can always provide the exact solutions in the prediction of the band gap of phononic crystals. In addition, the upper and lower solutions are always observed in the computation of the band gap of phononic crystals with the adjustment of α value. The performance of αFEM is compared with standard finite element method (FEM) with different types of mass matrix formulation. The numerical examples have strongly demonstrated that the αFEM has given more accuracy prediction in the analysis of phononic crystals compared with standard FEM.",

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N2 - In this paper, an alpha finite element method (αFEM) is formulated to study the propagation of elastic waves in periodic crystals. Using the simple triangular elements, the αFEM with optimal α value can always provide the exact solutions in the prediction of the band gap of phononic crystals. In addition, the upper and lower solutions are always observed in the computation of the band gap of phononic crystals with the adjustment of α value. The performance of αFEM is compared with standard finite element method (FEM) with different types of mass matrix formulation. The numerical examples have strongly demonstrated that the αFEM has given more accuracy prediction in the analysis of phononic crystals compared with standard FEM.

AB - In this paper, an alpha finite element method (αFEM) is formulated to study the propagation of elastic waves in periodic crystals. Using the simple triangular elements, the αFEM with optimal α value can always provide the exact solutions in the prediction of the band gap of phononic crystals. In addition, the upper and lower solutions are always observed in the computation of the band gap of phononic crystals with the adjustment of α value. The performance of αFEM is compared with standard finite element method (FEM) with different types of mass matrix formulation. The numerical examples have strongly demonstrated that the αFEM has given more accuracy prediction in the analysis of phononic crystals compared with standard FEM.

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SN - 0927-0256

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JO - Computational Materials Science

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ER -

An exact solution to compute the band gap in phononic crystals

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