含非完好界面的非线性弹性波超材料中SH波的非互易传输  

Nonreciprocal transmission for the SH wave in a nonlinear elastic wave metamaterial with imperfect interfaces

作　　者：李珍妮 王毅泽 汪越胜[1,2] Zhenni Li;Yize Wang;Yuesheng Wang(Institute of Engineering Mechanics,School of Civil Engineering,Beijing Jiaotong University,Beijing 100044,China;Department of Mechanics,School of Mechanical Engineering,Tianjin University,Tianjin 300350,China)

机构地区：[1]北京交通大学土木建筑工程学院力学系,北京100044 [2]天津大学机械工程学院力学系,天津300350

出　　处：《科学通报》2020年第8期695-703,共9页Chinese Science Bulletin

基　　金：国家自然科学基金(11532001);中德科学中心中德合作研究项目(GZ 1355);德国研究基金(ZH 15/27-1)资助。

摘　　要：研究了含非完好界面的非线性弹性波超材料中的非互易传输现象.通过结构的非对称性和材料的非线性打破了经典弹性波系统中的互易性原理.入射的反平面剪切(shear horizontal,SH)波与材料的非线性效应相互作用产生二次谐波.根据Bloch定理,利用刚度矩阵法得到了基频波和二次谐波的带隙和透射系数.通过与完好界面情况下的结果对比,讨论了界面特性对层状周期结构中SH波的带隙和非互易传输的影响.本研究有助于设计具有非互易传输性能的弹性波超材料器件.During the past decades,phononic crystals and elastic wave metamaterials as the artificial periodic structures have received considerable attention.Due to their distinguishing properties,these structures can be used for the wave energy manipulation,e.g.,band gaps,elastic wave cloaking and topological state,etc.Awell-known characteristic is the band gap which means that the elastic wave cannot propagate in some certain frequency regions.Based on this property,many engineering applications can be achieved,e.g.,filtering and wave isolation,etc.The investigations mentioned above are mainly focused on the linear elastic problems which cannot present the nonlinear wave properties.However,the nonlinearity appearing in the materials and structures can bring new and interesting wave phenomena.One of the nonlinear characteristics is the generation of the higher order harmonics.It can be applied to the nonlinear nondestructive testing.Recently,increasing attention has been focused on the nonlinear wave motion,which can result in the nonlinear band gap and acoustic diode.The new concept named as the acoustic diode has been presented by the combination of the band gap and material nonlinearity,which permits the wave propagation in only one direction.It can be achieved when the fundamental wave sits in the stop band but the second harmonic belongs to the pass band.However,the acoustic wave has one direction displacement component and usually propagates in the air or liquid.Thus we wonder whether the nonreciprocal phenomenon of the elastic wave can be achieved in the solid materials.The problem will become more interesting and necessary because of the coupling displacements with the vector characteristic in solids.In our previous work,we have discussed the nonreciprocal transmission for the incident SH and in-plane elastic waves in a nonlinear elastic wave metamaterial.The interface in the consecutive layers is always assumed as perfect,which means that the displacement and stress components are continuous across the interface.

关 键 词：非线性弹性波超材料 非互易传输 二次谐波 非完好界面 带隙 

分 类 号：TB34[一般工业技术—材料科学与工程] O735[理学—晶体学]