Flexible graphene smart electronics are a kind of electronic device made of silver or other inorganic material and a flexible graphene web substrate. Because of their flexibility and excellent electronic properties, flexible graphene smart electronics have become a research topic of interest. However, during the mass production process, the high-speed transmission of the continuous tension state is susceptible to external disturbances, which seriously restricts the improvement of the flexible graphene smart electronic printing speed. Therefore, studying the dynamic characteristics of moving flexible graphene electronic materials is of great significance for improving their quality and production efficiency. This paper considers a roll-to-roll smart RFID label graphene web as the research object. Based on the energy functional variational theory, the Bubnov-Galerkin method is used to eliminate the residual value of the dynamic Von Karman partial differential equation, and a discrete forced nonlinear vibration control equation for a moving flexible graphene smart electronic web is established. The Melnikov method is used to obtain the Melnikov function of the orbit parameter for the vibration control equation and solve the conditions of the chaos criterion. Using the fourth-order Runge-Kutta method, the nonlinear vibration phase-plane portraits, Poincare maps, time history diagram, and power spectra of the moving flexible graphene smart electronic web are obtained. The effects of the web moving speed, external damping, and initial system conditions on nonlinear dynamic behaviour are calculated, and the stable and unstable working regions of the moving flexible graphene smart electronic web are obtained. This research provides a theoretical basis for the dynamic stability and vibration control of a moving graphene smart electronic web.

柔性石墨烯智能电子产品是一种由银或其他无机材料和柔性石墨烯网状基材制成的电子设备。由于其柔性和出色的电子性能，柔性石墨烯智能电子已成为人们关注的研究课题。但是，在批量生产过程中，连续张紧状态的高速传输容易受到外界干扰，严重制约了柔性石墨烯智能电子印刷速度的提高。因此，研究移动柔性石墨烯电子材料的动力学特性对于提高其质量和生产效率具有重要意义。本文以卷对卷智能RFID标签石墨烯网为研究对象。根据能量功能变分理论，利用Bubnov-Galerkin方法消除了动态Von Karman偏微分方程的残值，建立了移动柔性石墨烯智能电子网的离散强迫非线性振动控制方程。梅尔尼科夫方法用于获得振动控制方程的轨道参数的梅尔尼科夫函数，并解决了混沌准则的条件。使用四阶Runge-Kutta方法，获得了移动柔性石墨烯智能电子网的非线性振动相平面肖像，庞加莱图，时间历史图和功率谱。计算了腹板移动速度，外部阻尼和初始系统条件对非线性动力学行为的影响，得到移动的柔性石墨烯智能电子网的稳定工作区和不稳定工作区。该研究为运动石墨烯智能电子网的动态稳定性和振动控制提供了理论依据。