基于几何积分方法的压电岛-桥结构动力行为分析  

DYNAMIC ANALYSIS OF PIEZOELECTRIC ISLAND-BRIDGE STRUCTURE BASED ON GEOMETRIC INTEGRAL METHOD

作　　者：鲁康 王博[1,4] 毕皓皓[2] 师岩 邓子辰[1,5] Lu Kang;Wang Bo;Bi Haohao;Shi Yan;Deng Zichen(Department of Engineering Mechanics,Northwestern Polytechnical University,Xi'an 710072,China;Department of Applied Mathematics,Northwestern Polytechnical University,xi'an 710072,China;State Key laboratory of Mechanics atul Control for Mechanical Structures,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China;State hey Laboratory of Industrial equipment structure Analysis,Dalian University of Technology,Dalian 116024,China;Ministry of Industry and Information Technology Key Laboratory of Dynamics and Control of Complex Systems,Northwestern Polytechnical University,Xi'an 710072,China)

机构地区：[1]西北工业大学工程力学系,西安710072 [2]西北工业大学应用数学系,西安710072 [3]南京航空航天大学机械结构力学及控制国家重点实验室,南京210016 [4]大连理工大学工业装备结构分析国家重点实验室,大连116024 [5]西北工业大学复杂系统动力学与控制工信部重点实验室,西安710072

出　　处：《动力学与控制学报》2022年第3期15-24,共10页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(11802319);机械结构力学及控制国家重点实验室开放课题资助项目(MCMS-E-0221K01)

摘　　要：基于岛一桥结构的柔性电子器件因其优越的延展性,在可穿戴皮肤电子和航空航天等领域展现出巨大的应用潜力.压电材料因其良好的电学和力学性能成为制造岛一桥结构蛇形互联导线的理想材料.然而,岛一桥结构的电子器件在工作过程中极易受温度激励等复杂物理场影响,产生非线性振动,会严重影响电子器件的稳定性和灵敏度.故而本文研究压电岛一桥结构的非线性动力学响应.首先,基于Timoshenko梁理论,建立两端固支的压电岛一桥结构偏微分振动控制方程;其次,利用Galerkin截断法,得到形式较为简单的常微分控制方程,并利用几何积分方法数值求解该常微分方程;最后,通过数值实验验证几何积分方法的有效性和优越性,讨论温度变化量和电压等参数对岛一桥结构动力学响应的影响规律.本文研究结果将为基于压电岛-桥结构的柔性电子器件的设计提供理论参考.Due to its excellent ductility, the flexible electronic device, which is based on the island-bridge structure, has wide applications in wearable skin electronics and aerospace. Lead zirconate titanate(PZT) is an ideal material to fabricate the island-bridge structure for flexible electronic devices, because of its excellent electrical and mechanical properties. However, those kinds of devices would work in a complex environment, and their stabilities would be influenced by the complex environment. Therefore, dynamic behaviors of the buckled island-bridge structure will be investigated in this paper. Firstly, based on the theory of Timoshenko beam, the governing equation of the buckled piezoelectric island-bridge structure with fixed ends is derived. Secondly, the Galerkin method is utilized to transform the partial differential equation into an ordinary differential equation. Thirdly, the geometric integral method is used to solve the corresponding dynamic equations. Finally, through several numerical examples, effectiveness and advantages of the geometric integral method are verified, and influences of temperature change and voltage on the dynamic response of the buckled island-bridge structure are discussed. The results of this paper would be useful to guide design of piezoelectric island-bridge-based flexible electronics.

关 键 词：岛-桥结构 TIMOSHENKO梁 几何积分方法 动态力学响应 

分 类 号：O175[理学—数学] TV384[理学—基础数学]