Heuristic model for closer estimating of lowest band gap in two- and three-dimensional ternary locally resonant phononic crystals

Wang Gang; Liu Yaozong; Shao Lihui

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Heuristic model for closer estimating of lowest band gap in two- and three-dimensional ternary locally resonant phononic crystals

Wang Gang 1 * #,Liu Yaozong 1 #,Shao Lihui 2 #

1.Institute of Mechatronical Engineering，National University of Defense Technology

2.Institute of Mechatronical Engineering-National University of Defense Technology

*Correspondence author

#Submitted by

Subject:

Funding: 国家自然科学基金（No.50575222）

Opened online:17 January 2006

Accepted by: none

Citation: Wang Gang,Liu Yaozong,Shao Lihui .Heuristic model for closer estimating of lowest band gap in two- and three-dimensional ternary locally resonant phononic crystals[OL]. [17 January 2006] http://en.paper.edu.cn/en_releasepaper/content/5031

Based on better understanding of the lattice vibration modes, two simple spring-mass models are constructed in order to estimate the frequencies on both the lower and upper edges of the lowest locally resonant band gaps of both the two- and three-dimensional ternary locally resonant phononic crystals. The parameters of the models are given in a reasonable way based on the physical insight of the band gap mechanism. Both the lumped-mass methods and our models are used in the study of the influences of structural and the material parameters on frequencies on both edges of the lowest gaps of in the two- and three-dimensional locally resonant phononic crystals. The analytical estimations with our models and the theoretical predictions with the lumped-mass method are in good agreement. The newly proposed heuristic models are helpful with better understanding of the locally resonant band gap mechanism, as well as better estimation of the band edge frequencies.

Keywords:Phononic crystal; Locally resonant; spring-mass model

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