Stability analysis of an electrically actuated microbeam using the Melnikov theorem and Poincaré mapping
Stability analysis of an electrically actuated microbeam using the Melnikov theorem and Poincaré mapping
复制标题
DOI：
10.1243/09544062jmes2273
复制
发表时间：
2011-02
期刊：
影响因子：
--
通讯作者：
M. Zamanian;S. E. Khadem
中科院分区：
文献类型：
--
作者：
M. Zamanian;S. E. Khadem
本文研究了电动驱动下微光束的稳定性。通过在微束和位于微束对面的极板之间施加电压来感应电致动。在微开关中，电致动作为直流电压施加，而在微谐振器中，它作为交流-直流电压的组合施加。假设微梁偏转时，其中间平面被拉伸。通过改变直流驱动作为微动开关系统的控制参数，可以观察到平衡解的稳定分支和不稳定分支在鞍节点分岔点相遇。用相平面图和庞卡罗映射法研究了微谐振腔的稳定性。结果表明，根据阻尼系数、交直流电压和微谐振器的其他参数，可以实现周期解、准周期解或拉入不稳定性。利用梅尔尼科夫定理研究了微谐振器可能混沌行为的预测。结果表明，虽然对于系统参数的选定区域，梅尔尼科夫函数满足混沌行为的发生，但对于这些参数值，在进入混沌行为之前，拉入不稳定性已经发生。简而言之，该系统不实现任何混沌行为。
In this article, the stability of a microbeam under an electric actuation is studied. The electric actuation is induced by applying a voltage between the microbeam and an electrode plate that lies at the opposite side of the microbeam. In microswitches, the electric actuation is applied as a DC voltage, and in microresonators it is applied as a combination of AC—DC voltages. It is assumed that the midplane of the microbeam is stretched when it is deflected. It is also shown that by the altering DC electric actuation as a control parameter in a microswitch system, a stable and an unstable branches of equilibrium solution is observed, which meet each other at a saddle-node bifurcation point. The stability of a microresonator is studied using the phase plane diagram and Poincaré mapping. It is shown that depending on the value of damping factor, AC and DC electric voltages, and other parameters of the microresonator, a periodic solution, a quasi periodic, or a pull-in instability may be realized. The prediction of possible chaotic behaviour for microresonator is studied using the Melnikov theorem. It is shown that although for selected domain of system parameters the Melnikov function is satisfied for occurrence of chaotic behaviour, for theses parameter values the pull-in instability occurs before going into the chaotic behaviour. Briefly, the system does not realize any chaotic behaviour.