三维波纹型可延展结构振动特性的辛分析

基于三维组装技术的可延展结构具备优异的延展性和可调控性，使其成功应用于各类可延展电子器件的制备中。为了评估该类电子器件的稳定性，本文研究三维波纹型可延展结构的振动行为。首先，基于非线性的Euler-Bernoulli梁理论、Kelvin-Voigt粘弹性理论和考虑压电材料的表面压电效应，建立三维波纹结构的理论分析模型；其次，基于能量原理和扩展拉格朗日运动原理，推导出该结构的动力学控制方程；然后采用二级四阶辛Runge-Kutta求解该动力学方程。通过数值仿真实验验证了辛算法的优越性，同时，还发现随着三维波纹型可延展结构外界激励及其结构参数的变化，该结构的振动特性会从倍周期向分岔和混沌转化；本文结果为三维波纹型可延展结构的优化设计及应用提供理论基础。

Symplectic analysis of vibration characteristics of three dimensional corrugated stretchable structures

Due to its excellent ductility and controllability,mechanically-assembled 3D structures are applied in the fabrication of stretchable electronic devices.In order to evaluate the stability of these stretchable electronic devices,the vibration behaviour of 3D corrugated stretchable structures is studied.Firstly,based on the nonlinear Euler-Bernoulli beam theory and Kelvin-Voigt viscoelastic theory,and considering the surface effect of the piezoelectric materials,the theoretical model of the 3D corrugated structure is established.Using the energy method and the extended Lagrange equation,the dynamic governing equations of the 3D stretchable structure are derived and these equations are solved by the symplectic Runge-Kutta method.The advantages of the symplectic algorithm are verified by numerical simulation experiments.The results show that by modulating the external excitation and structural parameters of the 3D stretchable piezoelectric structure,the vibration characteristics of this structure will transform from period doubling to chaos.The conclusions obtained in this paper will provide theoretical guidance for the optimal design and application of the 3D stretchable structures.