Study of band gaps of two-dimensional phononic crystals with criss-crossed elliptical holes

doi:10.3785/j.issn.1008-973X.2019.04.023

Journal of ZheJiang University (Engineering Science)

2019, Vol. 53

Issue (4): 811-818 DOI: 10.3785/j.issn.1008-973X.2019.04.023

Study of band gaps of two-dimensional phononic crystals with criss-crossed elliptical holes

Nan GAO1(

),Jian LI1,Rong-hao BAO1,2,3,*(

),Wei-qiu CHEN1,2,3

1. Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, China
2. Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou 310027, China
3. Soft Matter Research Center, Zhejiang University, Hangzhou 310027, China

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Abstract

The band gaps of elastic wave in two-dimensional phononic crystals with criss-crossed elliptical holes and the tunability of band gaps induced by the artificially introduced inclusions were analyzed through finite element method and experimental method. When the in-plane excitation is uniformly applied along the thickness of a thin phononic crystal plate, the dynamic response of the plate can be approximated as a plane-stress problem. Thin phononic plates with elliptical holes arrayed in a criss-cross pattern were analyzed with a two-dimensional finite element model based on the contrarian thinking in order to calculate the wave transmission along the ΓX direction of the reciprocal lattice. The effects of the ratio of major axis to minor axis, the porosity of holes, and the artificially introduced line defects on the band gaps and the wave propagation characteristics were systematically analyzed. The testing samples with the same dimensions as the numerical models were produced to conduct the transmission experiments. The numerical results accorded well with the experimental results. Results show that the width of band gap enlarges with the increasing of the ratio of major axis to minor axis, and the band gap can be reversely controlled by the insertion of line defects.

Key words： phononic crystal criss-crossed elliptical hole band gap elastic wave control

Received: 19 January 2018 Published: 28 March 2019

CLC:	TB 533
	O 735

Corresponding Authors: Rong-hao BAO E-mail: 21624008@zju.edu.cn;brh@zju.edu.cn

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Cite this article:

Nan GAO,Jian LI,Rong-hao BAO,Wei-qiu CHEN. Study of band gaps of two-dimensional phononic crystals with criss-crossed elliptical holes. Journal of ZheJiang University (Engineering Science), 2019, 53(4): 811-818.

URL:

http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2019.04.023 OR http://www.zjujournals.com/eng/Y2019/V53/I4/811

二维十字排列椭圆孔声子晶体带隙研究

采用有限元及实验方法，研究二维十字排列椭圆孔声子晶体中弹性波传播的带隙以及人为引入的夹杂对带隙的调控. 当声子晶体薄板沿板厚方向均匀施加面内激励时，将激发面内的动力响应，对应于平面应力状态. 基于逆向思维，针对二维十字排列椭圆孔声子晶体薄板，建立平面有限元模型，计算该模型沿晶格ΓX方向的波动传输特性，分析孔洞长短轴之比、孔隙率和线缺陷等因素对带隙及弹性波传播特性的影响. 制作与计算模型同尺寸的声子晶体试样进行传输特性实验，测试结果与有限元仿真结果吻合. 结果表明，带隙的宽度随着椭圆孔长短轴比例的增加而增大，可以通过引入合适的线缺陷来反向调控声子晶体的带隙.

关键词： 声子晶体, 十字排列椭圆孔, 带隙, 弹性波调控

Fig.1 Thin plate with criss-crossed elliptical holes

Fig.2 First Brillouin zone and irreducible Brillouin zone of squared lattice

Tab.1 Mechanical properties of testing sample

Fig.3 Band structure of phononic plate with criss-crossed elliptical holes

$(\phi = 50{\text{%}}, \kappa = 3.0)$

Fig.4 Locations of incentive point and receiving point

Fig.5 Comparison of band gap with transmission spectrum along ΓX direction

Fig.6 PMMA sample with criss-crossed elliptical holes

Fig.7 Schema of wave propagation test system

Fig.8 Wave propagation test setup

Fig.9 Transmission spectrum along ΓX direction by numerical method and experiment for phononic crystals with circular holes

$(\phi = 50{\text{%}} ,\;\kappa = 1.0)$

Fig.10 Effect of ratio of major axis to minor axis on band gap along ΓX direction

Fig.11 Effect of porosity on band gap along ΓX direction

Fig.12 Wave modes at lower edge of band gap with different ratios of major axis to minor axis when

$\phi =50{\text{%}}$

Fig.13 Mass-ligament models

Fig.14 Contour plots of displacement for phononic crystal plate

Fig.15 Two kinds of line defect

Fig.16 Effects of line defects on transmission

Fig.17 Effects of defects on wave propagation under 10.1 kHz


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