温度场下波纹型薄膜基底结构的动态屈曲分析  

Dynamic Buckling Analysis of Wrinkled Film Substrate Structure under the Thermal Effect

作　　者：李文杰 毕皓皓 张欣刚 姚文莉[1] 王博[2] Li Wenjie;Bi Haohao;Zhang Xingang;Yao Wenli;Wang Bo(School of Science,Qingdao University of Technology,Qingdao 266520,China;Department of Engineering Mechanics,Northwestern Polytechnical University,Xi’an 710072,China)

机构地区：[1]青岛理工大学理学院,青岛266520 [2]西北工业大学工程力学系,西安710072

出　　处：《动力学与控制学报》2024年第10期77-83,共7页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(12172282,12272197,12402002);广东省自然科学基金(2024A1515010767);山东省自然科学基金(ZR2022MA066)。

摘　　要：基于薄膜/基底结构的柔性电子器件具有良好的可拉伸性和灵敏度,然而此类结构电子器件的动力学行为极易受到温度变化等激励的影响.因此,本文研究了温度场作用下薄膜/基底结构的动态屈曲问题.首先,基于Euler-Bernoulli梁理论,建立温度场作用下,薄膜/基底结构非线性振动的控制方程;其次,利用Galerkin截断方法和两类变量,将薄膜/基底结构非线性振动的控制方程导入Hamilton体系;最后,通过高精度、高数值稳定性的辛Runge-Kutta方法求解薄膜/基底结构的Hamilton方程,进而讨论温度变化量、阻尼系数等对薄膜/基底结构非线性动力学响应的影响.研究发现薄膜的温度变化量和预应变会影响薄膜的动力学行为.随着温度变化量的增加,薄膜/基底结构的振动频率增加,振幅减小.随着预应变的增加,结构的频率减小,振幅增加.Flexible electronic devices,which are based on thin film/substrate structure,have excellent stretchability and sensitivity,but the dynamic behaviour of this film/substrate structure is very susceptible to the complex excitation such as temperature change.Therefore,the dynamic buckling behaviour of thin film/substrate structure under the thermal effect is studied in this paper.Firstly,based on Euler-Bernoulli beam theory,the governing equations of nonlinear vibration of thin film/substrate structure under the thermal effect are established.Secondly,the governing equations of nonlinear vibration of thin film/substrate structures are introduced into Hamilton system by the Galerkin method.Finally,the Hamilton equation of the thin film/substrate structure is solved by the Symplectic Runge-Kutta method,and the influence of temperature variation and damping coefficient on the nonlinear dynamic response of the thin film/substrate structure is discussed.It is found that the temperature variation and the pre-strain could change the dynamic behaviour of the thin film/substrate structure.With the increase of temperature variation,the vibration frequency of the film/substrate structure increases and the amplitude decreases.With the increase of pre-strain,the frequency of the system decreases and the amplitude increases.

关 键 词：薄膜/基底结构 EULER-BERNOULLI梁 辛Runge-Kutta方法 温度影响 

分 类 号：O322[理学—一般力学与力学基础] O175[理学—力学]