基于辛Runge-Kutta方法的棋盘形褶皱二维薄膜-基底结构动力学特性研究  

Dynamic behaviour of 2D film-substrate structure with checkerboard regime via Symplectic Runge-Kutta method

作　　者：张博涵 曹善成 王博[1,4] 欧阳华江[3] 徐方暖 ZHANG Bo-han;CAO Shan-cheng;WANG Bo;OUYANG Hua-jiang;XU Fang-nuan(Department of Engineering Mechanics,Northwestern Polytechnical University,Xi’an 710072,China;School of Astronautics,Northwestern Polytechnical University,Xi’an 710072,China;School of Mechanical Engineering,Southwest Jiaotong University,Chengdu 610031,China;State Key Laboratory of Structural Analysis,Optimization and CAE Software for Industrial Equipment,Dalian University of Technology,Dalian 116024,China)

机构地区：[1]西北工业大学工程力学系,西安710072 [2]西北工业大学航天学院,西安710072 [3]西南交通大学机械工程学院,成都610031 [4]大连理工大学工业装备结构分析优化与CAE软件全国重点实验室,大连116024

出　　处：《计算力学学报》2024年第1期186-193,共8页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(12172282,12102346);中央高校基本科研业务费专项资金资助项目.

摘　　要：基于力学屈曲原理的褶皱薄膜-基底结构已成功应用于制备可延展无机电子器件。然而,该类电子器件在应用时需要服役于复杂动态环境中,针对棋盘形褶皱薄膜结构的动力学问题鲜有研究,此问题又是该类电子器件走向实际应用需要解决的关键问题之一。本文首先采用能量方法,分别计算了二维薄膜的弯曲能、膜弹性能和柔性基底中的弹性能以及薄膜动能;然后采用拉格朗日方程,推导出了该结构的振动控制方程;而该方程为非线性动力学方程,无法给出其解析解;因此,本文采用辛Runge-Kutta方法对其进行数值求解;数值结果表明,辛数值方法具有长期稳定的特性和系统结构特性,为高精度的可延展电子器件的动力学问题研究提供了优异的数值方法。Stretchable inorganic electronics,based on buckling mechanisms,have been fabricated.However,these electronics need to work in a dynamic environment and the dynamic behaviour of these structures is also one of important considerations for their applications in industry.In this paper,the potential energies due to bending and in-plane membrane deformation of the 2D film,and the kinetic energy and the potential energy of the compressed substrate of a film-substrate structure are formulated;then,by using the Lagrange equation,the governing equation of this buckled structure his derived.Since the analytical solutions of this equation cannot be obtained,it is solved by the Symplectic Runge-Kutta method.Through the numerical examples,it is found that the Symplectic algorithm can preserve the characteristics of the film-substrate structure in long-time,and also maintain the buckling characteristics,and thus provides an excellent numerical analysis method for determining dynamic behaviour of stretchable inorganic,buckled film-substrate-based electronics.

关 键 词：可延展电子器件 薄膜-基底结构 辛算法 保结构 

分 类 号：O313[理学—一般力学与力学基础] O302[理学—力学]