论文标题
石墨烯板的非线性振荡和共振现象的频谱
Frequency spectrum of nonlinear oscillations and resonance phenomena for graphene plates
论文作者
论文摘要
论文研究石墨烯板的振荡，即变形远远超过板的厚度。在这种最现实的情况下，振荡是由非线性部分微分方程（Foppl-von karman方程）的系统描述的。该系统被简化为一个非线性普通微分方程，并通过Bogoliubov-Mitropolsky渐近方法进行了研究。结果，我们具有矩形石墨烯板的实际频率谱。接下来，我们检查了强制振荡下的非线性共振效应。这些结果可以适用于可变应变诱导的假磁场。这样的字段允许更好地了解与运输过程相关的挠性声子的特性。共振现象在石墨烯板在工程结构中的应用中起主要作用。
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.
