Abstract

The present article aims to clarify the effect of the nanoflow on the nonlinear dynamic instability of graphene sheets under parametric excitation. To achieve this aim, the graphene layer is added to a visco-Pasternak foundation then, the resulting nanostructure is subjected to the nanoflow and a parametric axial force, simultaneously. The nonlocal elasticity and the nonlinear von Karman theories and Hamilton’s principle are combined in this article, which lead to the governing equation of motion. A class of nonlinear Mathieu–Hill equation is established to determine the bifurcations and the regions of the nonlinear dynamic instability. The main conclusion to be drawn is that nanoflow directly influences the amplitude response of the system. This investigation contains analysis of how the nanoflow affects the nonlinear instability of nanostructures including the graphene sheets which can be provided useful information for the next investigations in field of nano electromechanical system.

摘要

本文旨在阐明纳米流对参数激发下石墨烯片非线性动态不稳定性的影响。为了实现这一目标，石墨烯层被添加到粘胶-帕斯捷尔纳克基础上，所得纳米结构同时受到纳米流动和参数轴向力的作用。本文将非局部弹性与非线性von Karman理论和Hamilton原理相结合，得出了运动的控制方程。建立了一类非线性Mathieu-Hill方程来确定非线性动态不稳定性的分岔和区域。要得出的主要结论是纳流直接影响系统的幅度响应。