Theoretical and Experimental Investigation of Two-to-One Internal Resonance in MEMS Arch Resonators
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AbstractWe 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.
CitationAlfosail F, Hajjaj AZ, Younis M (2018) Theoretical and Experimental Investigation of Two-to-One Internal Resonance in MEMS Arch Resonators. Journal of Computational and Nonlinear Dynamics. Available: http://dx.doi.org/10.1115/1.4041771.
SponsorsWe acknowledge the financial support of King Abdullah University of Science and Technology and Saudi Aramco.