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首页> 外文期刊>International journal of structural stability and dynamics >An Analytical Study for Nonlinear Free and Forced Vibration of Electrostatically Actuated MEMS Resonators
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An Analytical Study for Nonlinear Free and Forced Vibration of Electrostatically Actuated MEMS Resonators

机译：静电驱动MEMS谐振器非线性自由振动的分析研究

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This work aims to construct accurate and simple lower-order analytical approximation solutions for the free and forced vibration of electrostatically actuated micro-electro-mechanical system (MEMS) resonators, in which geometrical and material nonlinearities are induced by the mid-plane stretching, dynamic pull-in characteristics, electrostatic forces and other intrinsic properties. Due to the complexity of nonlinear MEMS systems, the quest of exact closed-form solutions for these problems is hardly obtained for system design and analysis, in particular for harmonically forced nonlinear systems. To examine the simplicity and effectiveness of the present analytical solutions, two illustrative cases are taken into consideration. First, the free vibration of a doubly clamped microbeam suspended on an electrode due to a suddenly applied DC voltage is considered. Based on the Euler Bernoulli beam theory and the von Karman type nonlinear kinematics, the dynamic motion of the microbeam is further discretized by the Galerkin method to an autonomous system with general nonlinearity, which can be solved analytically by using the Newton harmonic balance method. In addition to large amplitude free vibration, the primary resonance response of a doubly clamped microbeam driven by two symmetric electrodes is also investigated, in which the microbeam is actuated by a bias DC voltage and a harmonic AC voltage. Following the same decomposition approach, the governing equation of a harmonically forced beam model can be transformed to a non autonomous system with odd nonlinearity only. Then, lower-order analytical approximation solutions are derived to analyze the steady-state resonance response of such a problem under a combination of various DC and AC voltage effects. Finally, the analytical approximation results of both cases are validated, and they are in good agreement with those obtained by the standard Runge-Kutta method.
机译：这项工作旨在为静电致动的微机电系统（MEMS）谐振器的自由和强制振动构建精确和简单的低阶分析近似解，其中由中间平面伸展，动态诱导几何和材料非线性拉伸特性，静电力和其他内在特性。由于非线性MEMS系统的复杂性，对于系统的设计和分析，几乎不得获得对这些问题的确切闭合液解决方案的任务，特别是对于谐波强制非线性系统。为了检查本分析解决方案的简单性和有效性，考虑了两种说明性情况。首先，考虑由于突然施加的DC电压悬浮在电极上的双夹紧微沟的自由振动。基于欧拉伯努利光束理论和von Karman型非线性运动学，通过Galerkin方法对具有一般非线性的自治系统进一步离散的Microbeam的动态运动，这可以通过使用牛顿谐波平衡法分析。除了大的幅度自由振动之外，还研究了由两个对称电极驱动的双夹紧微观的初级谐振响应，其中通过偏置直流电压和谐波AC电压致动微波。在相同的分解方法之后，可以仅具有奇数非线性的非自治系统转换谐波强制光束模型的控制方程。然后，导出较低的分析近似解，以分析各种DC和AC电压效应的组合下这种问题的稳态共振响应。最后，验证了这两种情况的分析近似结果，它们与标准跑为库方法获得的那些吻合良好。

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