The nonlinear vibration of a nanobeam under electrostatic force is investigated through the nonlocal strain gradient theory. Using Galerkin method, the partial differential equation of motion is reduced to an ordinary nonlinear differential one. The equivalent linearization method with a weighted averaging and a variational approach are used independently to establish the frequency–amplitude relationship under closed-forms for comparison purpose. Effects of material and operational parameters on the frequency ratio (the ratio of nonlinear frequency to linear frequency), on the nonlinear frequency, and on the stable configuration of the nanobeam are studied and discussed.

中文翻译：

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基于非局部应变梯度理论的纳米束在静电作用下的非线性振动

通过非局部应变梯度理论研究了纳米束在静电作用下的非线性振动。使用Galerkin方法，将运动的偏微分方程简化为普通的非线性微分方程。分别使用带加权平均的等效线性化方法和变分方法来建立封闭形式下的频率-振幅关系，以进行比较。研究和讨论了材料和操作参数对频率比（非线性频率与线性频率之比），非线性频率以及纳米束稳定配置的影响。