Abstract A nonlocal elasticity theory is a popular growing technique for mechanical analysis of the micro- and nanoscale structures which captures the small-size effects. In this paper, a comprehensive study was carried out to investigate the influence of the nonlocal parameter on the bifurcation behavior of a capacitive clamped-clamped nano-beam in the presence of the electrostatic and centrifugal forces. By using Eringen’s nonlocal elasticity theory, the nonlocal equation of the dynamic motion for a nano-beam has been derived using Euler–Bernoulli beam assumptions. The governing static equation of motion has been linearized using step by step linearization method; then, a Galerkin based reduced order model have been used to solve the linearized equation. In order to study the bifurcation behavior of the nano-beam, the static non-linear equation is changed to a one degree of freedom model using a one term Galerkin weighted residual method. So, by using a direct method, the equilibrium points of the system, including stable center points, unstable saddle points and singular points have been obtained. The stability of the fixed points has been investigated drawing motion trajectories in phase portraits and basins of attraction set and repulsion have been illustrated. The obtained results have been verified using the results of the prior studies for some cases and a good agreement has been observed. Moreover, the effects of the different values of the nonlocal parameter, angular velocity and van der Waals force on the fixed points have been studied using the phase portraits of the system for different initial conditions. Also, the influence of the nonlocal beam theory and centrifugal forces on the dynamic pull-in behavior have been investigated using time histories and phase portraits for different values of the nonlocal parameter.

中文翻译：

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基于非局域理论的考虑离心力的静电驱动纳米梁分岔分析

摘要 非局部弹性理论是一种流行的技术，用于捕捉小尺寸效应的微米和纳米级结构的力学分析。在本文中，进行了一项综合研究，以研究在静电和离心力存在下非局部参数对电容夹钳纳米梁分叉行为的影响。通过使用 Eringen 的非局部弹性理论，已经使用 Euler-Bernoulli 梁假设导出了纳米梁动态运动的非局部方程。控制静态运动方程已采用逐步线性化方法线性化；然后，使用基于伽辽金的降阶模型来求解线性化方程。为了研究纳米光束的分岔行为，使用单项伽辽金加权残差法将静态非线性方程改为单自由度模型。因此，采用直接法得到了系统的平衡点，包括稳定中心点、不稳定鞍点和奇异点。已经研究了不动点的稳定性，绘制了相图中的运动轨迹，并说明了引力集和斥力的盆地。所获得的结果已经使用先前研究的结果在某些情况下得到验证，并且已经观察到良好的一致性。此外，利用系统在不同初始条件下的相图，研究了非局部参数、角速度和范德华力的不同值对不动点的影响。还，