Nonlinear dynamics of an electrically actuated imperfect microbeam resonator: experimental investigation and reduced-order modeling
Nonlinear dynamics of an electrically actuated imperfect microbeam resonator: experimental investigation and reduced-order modeling
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DOI：
10.1088/0960-1317/23/7/075012
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发表时间：
2013-06
影响因子：
2.3
通讯作者：
Laura Ruzziconi;A. Bataineh;M. Younis;W. Cui;S. Lenci
中科院分区：
文献类型：
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作者：
Laura Ruzziconi;A. Bataineh;M. Younis;W. Cui;S. Lenci
研究了由不完全固支微梁组成的微电子机械系统(MEMS)器件在静电和电动激励下的动态行为。我们的目标是开发一种理论分析，能够描述和预测实验反应的所有主要相关方面。进行了广泛的实验研究，发现了来自微加工的主要缺陷，识别了前四个实验固有频率，并在第一对称共振附近探索了随着电动激励值的增加而产生的非线性动力学。获得了几次后向和前向频率扫描。突出了非线性行为，包括多稳态的范围，其中非共振和共振分支共存，以及超谐共振清晰可见的间隔。进行了数值模拟。首先，考虑了两个单模降阶模型。一种是通过Galerkin技术产生的，另一种是通过结合使用Ritz方法和Padé近似来产生的。两者都能与实验数据提供令人满意的一致性。这不仅在低电激值时发生，而且在高电激值时也会发生。详细讨论了它们的计算效率，因为这是系统的局部和全局模拟的一个重要方面。最后，进一步完善了理论分析，建立了一个二自由度降阶模型，该模型也能够捕获测量到的二次对称超谐共振。尽管表面上看起来很简单，但所有提出的降阶模型都能够准确和恰当地描述实验装置的复杂非线性动力学，这验证了所提出的理论方法。
We present a study of the dynamic behavior of a microelectromechanical systems (MEMS) device consisting of an imperfect clamped–clamped microbeam subjected to electrostatic and electrodynamic actuation. Our objective is to develop a theoretical analysis, which is able to describe and predict all the main relevant aspects of the experimental response. Extensive experimental investigation is conducted, where the main imperfections coming from microfabrication are detected, the first four experimental natural frequencies are identified and the nonlinear dynamics are explored at increasing values of electrodynamic excitation, in a neighborhood of the first symmetric resonance. Several backward and forward frequency sweeps are acquired. The nonlinear behavior is highlighted, which includes ranges of multistability, where the nonresonant and the resonant branch coexist, and intervals where superharmonic resonances are clearly visible. Numerical simulations are performed. Initially, two single mode reduced-order models are considered. One is generated via the Galerkin technique, and the other one via the combined use of the Ritz method and the Padé approximation. Both of them are able to provide a satisfactory agreement with the experimental data. This occurs not only at low values of electrodynamic excitation, but also at higher ones. Their computational efficiency is discussed in detail, since this is an essential aspect for systematic local and global simulations. Finally, the theoretical analysis is further improved and a two-degree-of-freedom reduced-order model is developed, which is also capable of capturing the measured second symmetric superharmonic resonance. Despite the apparent simplicity, it is shown that all the proposed reduced-order models are able to describe the experimental complex nonlinear dynamics of the device accurately and properly, which validates the proposed theoretical approach.