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浙江大学学报(工学版)
浙江大学学报(工学版)  2019, Vol. 53 Issue (4): 811-818    DOI: 10.3785/j.issn.1008-973X.2019.04.023
工程力学     
二维十字排列椭圆孔声子晶体带隙研究
高楠1(),李剑1,鲍荣浩1,2,3,*(),陈伟球1,2,3
1. 浙江大学 工程力学系，浙江 杭州 310027
2. 浙江大学 浙江省软体机器人与智能器件研究重点实验室，浙江 杭州 310027
3. 浙江大学 软物质科学研究中心，浙江 杭州 310027
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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摘要：

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    
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
收稿日期: 2018-01-19 出版日期: 2019-03-28
CLC:  TB 533  
通讯作者: 鲍荣浩     E-mail: 21624008@zju.edu.cn;brh@zju.edu.cn
作者简介: 高楠（1994—），女，硕士生，从事声子晶体的研究. orcid.org/0000-0002-4943-7217. E-mail： 21624008@zju.edu.cn
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引用本文:

高楠,李剑,鲍荣浩,陈伟球. 二维十字排列椭圆孔声子晶体带隙研究[J]. 浙江大学学报(工学版), 2019, 53(4): 811-818.

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.

链接本文:

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

图 1  十字排列椭圆孔薄板结构
图 2  正方晶格的第一布里渊区及不可约布里渊区
材料 ρ/（g·cm?3） E/GPa μ
亚克力（PMMA） 1.18 2.7 0.4
表 1  试样材料参数
图 3  十字椭圆孔声子板的能带结构 $(\phi = 50{\text{%}}, \kappa = 3.0)$
图 4  激励点与接收点位置示意图
图 5  在ΓX方向上，声子晶体能带结构与传输谱对比
图 6  十字排列椭圆孔PMMA试样
图 7  波动测试系统示意图
图 8  波动测试系统实景图
图 9  十字排列圆孔声子晶体ΓX方向透射谱实验与有限元结果对比 $(\phi = 50{\text{%}}, \;\kappa = 1.0)$
图 10  孔洞长短轴之比对ΓX方向带隙的影响
图 11  结构孔隙率对ΓX方向带隙的影响
图 12   $\phi =50 {\text{%}}$ 时，不同长短轴之比带隙下边界的振动模态
图 13  质量块-韧带等效结构示意图
图 14  声子晶体薄板的波动位移分布
图 15  2种线缺陷
图 16  线缺陷对传输谱的影响
图 17  10.1 kHz频率下，缺陷的引入对波传播的影响
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