Theoretical and experimental investigations of the crossover phenomenon in micromachined arch resonator: part II—simultaneous 1:1 and 2:1 internal resonances
Online Publication Date2019-09-27
Print Publication Date2020-01
Embargo End Date2020-09-27
Permanent link to this recordhttp://hdl.handle.net/10754/656931
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AbstractWe investigate in a silicon micromachined arch beam the activation of a one-to-one internal resonance between the first symmetric and first antisymmetric modes simultaneously with the activation of a two-to-one internal resonance between these modes and the second symmetric mode. The arch is excited electrically, using an antisymmetric partial electrode to activate both modes of vibrations, and tuned electrothermally via Joule’s heating. Theoretically, we explore the dynamics of the beam using the Galerkin and multiple timescales methods. The simulation results are shown to have good agreement with the experimental data. The results show the merging of both modes at crossing, after which the first antisymmetric mode exchanges the nonlinear behavior with the first symmetric mode. The nonlinear behavior of the arch beam is demonstrated and analyzed experimentally and theoretically as experiencing the simultaneous 2:1 and 1:1 internal resonances.
CitationHajjaj, A. Z., Alfosail, F. K., Jaber, N., Ilyas, S., & Younis, M. I. (2019). Theoretical and experimental investigations of the crossover phenomenon in micromachined arch resonator: part II—simultaneous 1:1 and 2:1 internal resonances. Nonlinear Dynamics. doi:10.1007/s11071-019-05242-9
SponsorsWe acknowledge the financial support from King Abdullah University of Science and Technology (KAUST).
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Theoretical and Experimental Investigation of Two-to-One Internal Resonance in MEMS Arch ResonatorsAlfosail, Feras; Hajjaj, Amal; Younis, Mohammad I. (Journal of Computational and Nonlinear Dynamics, ASME International, 2018-11-19) [Article]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 multi-mode Galerkin procedure and to expermental 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.
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Efficient primary and parametric resonance excitation of bistable resonatorsRamini, Abdallah; Alcheikh, Nouha; Ilyas, Saad; Younis, Mohammad I. (AIP Advances, AIP Publishing, 2016-09-12) [Article]We experimentally demonstrate an efficient approach to excite primary and parametric (up to the 4th) resonance of Microelectromechanical system MEMS arch resonators with large vibrational amplitudes. A single crystal silicon in-plane arch microbeam is fabricated such that it can be excited axially from one of its ends by a parallel-plate electrode. Its micro/nano scale vibrations are transduced using a high speed camera. Through the parallel-plate electrode, a time varying electrostatic force is applied, which is converted into a time varying axial force that modulates dynamically the stiffness of the arch resonator. Due to the initial curvature of the structure, not only parametric excitation is induced, but also primary resonance. Experimental investigation is conducted comparing the response of the arch near primary resonance using the axial excitation to that of a classical parallel-plate actuation where the arch itself forms an electrode. The results show that the axial excitation can be more efficient and requires less power for primary resonance excitation. Moreover, unlike the classical method where the structure is vulnerable to the dynamic pull-in instability, the axial excitation technique can provide large amplitude motion while protecting the structure from pull-in. In addition to primary resonance, parametrical resonances are demonstrated at twice, one-half, and two-thirds the primary resonance frequency. The ability to actuate primary and/or parametric resonances can serve various applications, such as for resonator based logic and memory devices. (C) 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license