石墨烯板非线性振动和共振现象的频谱
Frequency spectrum of nonlinear oscillations and resonance phenomena for graphene plates
摘要：
在变形量远大于板厚的假设下，研究了石墨烯板的振动。在这种最现实的情况下，振荡由非线性偏微分方程（Foppl-von Karman方程）系统描述。将该系统化为一个非线性常微分方程，并利用Bogoliubov-Mitropolsky渐近方法进行研究。结果，我们得到了矩形石墨烯板的真实频谱。其次，我们研究了强迫振动下的非线性共振效应。这些结果可以适用于可变应变引起的伪磁场。这样的领域允许更好地理解与输运过程有关的弯曲声子的性质。共振现象在石墨烯板在工程建设中的应用中起着主导作用。
英文摘要：
The paper studies oscillations of graphene plates under the hypothesis that deformations are much more than the thickness of plate. In this most realistic case the oscillations are described by the system of nonlinear partial differential equations (the Foppl-von Karman equations). This system is reduced to one nonlinear ordinary differential equation and investigated by means of the Bogoliubov-Mitropolsky asymptotic methods. As a result, we have the real frequency spectrum for rectangular graphene plates. Next we have examined the nonlinear resonance effects under forced oscillations. These outcomes can apply for variable strain-induced pseudomagnetic fields. Such fields permit better to understand the properties of flexural phonons connected with transport process. Resonance phenomena play a leading role in application of graphene plates in engineering constructions.
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