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

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.