局域共振型声子晶体梁的动态模型和带隙  

Dynamic Model and Band Gaps of Locally Resonant Phononic Crystal Beams

作　　者：汤璐嘉 吕延军[1,2] 刘成 郭城[1] TANG Lujia;LYU Yanjun;LIU Cheng;GUO Cheng(School of Mechanical and Precision Instrument Engineering,Xi′an University of Technology Xi′an,710048,China;State Key Laboratory of Digital Manufacturing Equipment and Technology,Huazhong University of Science and Technology Wuhan,430074,China)

机构地区：[1]西安理工大学机械与精密仪器工程学院,西安710048 [2]华中科技大学数字制造装备与技术国家重点实验室,武汉430074

出　　处：《振动．测试与诊断》2021年第6期1132-1137,1238,共7页Journal of Vibration,Measurement & Diagnosis

基　　金：国家自然科学基金资助项目(51775428);陕西省重点研发计划资助项目(2020GY-06);数字制造装备与技术国家重点实验室开放课题资助项目(DMETKF2017014)。

摘　　要：建立了一种具有边界条件的局域共振型声子晶体梁的理论模型,其中声子晶体简支梁连接有周期分布的弹簧振子结构。根据Hamilton原理得到了该结构的动力学方程,采用Rayleigh-Ritz方法求得了该结构的动态特性以及局域共振型带隙的数值结果。所得到的结果同已有文献中的实验结果具有较好的一致性,说明所提出的理论模型是可行的。根据所建立的理论模型,分析了梁的长度和晶格常数对带隙的影响。可以看出:当声子晶体的晶格常数相对于梁的长度较小时,结构的频响特性中具有明显的带隙,在弹簧振子的固有频率处有反共振峰出现,并且始终位于带隙范围内;而当晶格常数相对于梁的长度较大时,结构的带隙情况较为复杂,且受边界条件的影响较大。The paper aims to construct a theoretical model on locally resonant phononic crystal beams with boundary conditions.In the model,a simply supported beam is attached to periodic spring-mass systems.In terms of the Hamilton′s principle,the dynamic equation of the model is formulated in theory.Further,the dynamic characteristics and locally resonant band gaps of the model are achieved by using the Rayleigh-Ritz method.The numerical results agree well with the experimental data in the previous literature,indicating that the presented model is feasible in theory.According to the presented model,band gaps of the phononic crystal beams considering different beam lengths and lattice constants are investigated.When the lattice constant of the periodic structure is smaller than the beam length,band gaps in frequency response curves are distinctly observed.Besides,there are anti-resonant crests located in the band gaps which correspond to the natural frequency of a spring-mass system.On the other hand,the band gaps are complicated and heavily influenced by the boundary condition if the lattice constant increases.

关 键 词：简支梁 声子晶体 弹簧振子系统 局域共振型带隙 

分 类 号：TH113.1[机械工程—机械设计及理论]