Theoretical and Experimental Investigation of Two-to-One Internal Resonance in MEMS Arch Resonators
Theoretical and Experimental Investigation of Two-to-One Internal Resonance in MEMS Arch Resonators
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DOI：
10.1115/1.4041771
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发表时间：
2019-01-01
影响因子：
2
通讯作者：
Younis, Mohammad I.
中科院分区：
文献类型：
--
作者：
Alfosail, Feras K.;Hajjaj, Amal Z.;Younis, Mohammad I.
从理论和实验上研究了电热调谐和静电驱动的微机械拱梁中的二比一内共振。通过在拱门两端施加电热电压，它的前两个对称模式之间的比率被调到两个。用多尺度摄动法模拟了拱梁在二比一内共振过程中的非线性响应。在较高交流电压下，考虑二次非线性、三次非线性和两个同时激励的影响，将摄动解扩展到三阶。将微扰解与多模Galerkin方法得到的结果以及基于特制的硅拱梁的实验数据进行了比较。结果表明，两者吻合较好。结果表明，系统表现出不同类型的分叉，如鞍点分叉和Hopf分叉，这些分叉可以导致准周期运动和潜在的混沌运动。
We investigate theoretically and experimentally the two-to-one internal resonance in micromachined arch beams, which are electrothermally tuned and electrostatically driven. By applying an electrothermal voltage across the arch, the ratio between its first two symmetric modes is tuned to two. We model the nonlinear response of the arch beam during the two-to-one internal resonance using the multiple scales perturbation method. The perturbation solution is expanded up to three orders considering the influence of the quadratic nonlinearities, cubic nonlinearities, and the two simultaneous excitations at higher AC voltages. The perturbation solutions are compared to those obtained from a multimode Galerkin procedure and to experimental data based on deliberately fabricated Silicon arch beam. Good agreement is found among the results. Results indicate that the system exhibits different types of bifurcations, such as saddle node and Hopf bifurcations, which can lead to quasi-periodic and potentially chaotic motions.