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Nonlinear membrane model for large amplitude vibration of single layer graphene sheets

机译：单层石墨烯片大振幅振动的非线性膜模型

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摘要

The nonlinear vibrational properties of single layer graphene sheets (SLGSs) are investigated using a membrane model. The nonlinear equation of motion is considered for the SLGSs by including the effects of stretching due to large amplitudes. The equation of motion is numerically solved utilizing the finite difference method for SLGSs with different initial and boundary conditions, sizes and pretensions. It is concluded that the nonlinear fundamental frequency of SLGSs increases by increasing the pretension and initial velocity. In addition, it is observed that an increase in the pretension weakens the effects of the initial velocity on the fundamental frequency, such that the fundamental frequency approximately becomes independent of the initial velocity. This is an important feature of the vibrating systems consisting of SLGSs which are used in the nano-electromechanical systems (NEMS), where resonators with a specific fundamental frequency and independent of the initial velocity are of interest
机译：使用膜模型研究了单层石墨烯片（SLGSs）的非线性振动特性。通过包括由于大振幅引起的拉伸效应，可以考虑SLGS的非线性运动方程。对于具有不同初始和边界条件，大小和预张力的SLGS，使用有限差分法对运动方程进行数值求解。结论是，SLGSs的非线性基频通过增加预紧力和初始速度而增加。另外，观察到预紧力的增加削弱了初始速度对基频的影响，使得基频近似变得与初始速度无关。这是由用于纳米机电系统（NEMS）的SLGS组成的振动系统的重要特征，其中感兴趣的是具有特定基本频率且与初始速度无关的谐振器

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