Small size (micro/nano)‐scale beams constitute important building blocks of microelectromechanical systems (MEMS)/nanoelectromechanical systems (NEMS). Emerging roll‐based, high rate, manufacturing processes can make these small size‐beams vibrate, while they are axially moving. In this paper, an analytical‐numerical study on the nonlinear transverse vibration of the representative case of axially moving micro‐beam under an electrostatic force is conducted. The analytical model is realized by employing Hamilton's principle together with Galerkin discretization. The method of multiple time‐scales and Runge‐Kutta based numerical scheme are utilized to investigate the nonlinear dynamic behavior of the micro‐beam. Results are obtained for the influence of axial beam velocity and modified couple stress theory length scale parameter (i) on the values of pull‐in instability voltage of the small‐size beam, and (ii) on the small‐size beam nonlinear softening/hardening characteristics. The effect of axial load on the frequency response is investigated.

中文翻译：

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静电作用下轴向振动的小梁的非线性行为

小尺寸（微/纳米）级光束是微机电系统（MEMS）/纳米机电系统（NEMS）的重要组成部分。新兴的基于辊的高速率制造工艺可使这些小尺寸的梁在轴向移动时发生振动。在本文中，对轴向运动的微束在静电力作用下的典型情况的非线性横向振动进行了解析数值研究。通过采用汉密尔顿原理和Galerkin离散化来实现分析模型。利用多个时标方法和基于Runge-Kutta的数值方案来研究微束的非线性动力学行为。得出了以下结果：轴向梁速度和改进的耦合应力理论长度尺度参数（i）对小尺寸梁的拉入不稳定性电压值的影响，以及（ii）对小尺寸梁非线性软化/硬化特性。研究了轴向载荷对频率响应的影响。