Theoretical and experimental investigations of the crossover phenomenon in micromachined arch resonator: part II—simultaneous 1:1 and 2:1 internal resonances

Amal Hajjaj, Feras Alfosail, Nizar Jaber, Saad Ilyas, Mohammad I. Younis

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We 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.
Original languageEnglish (US)
Pages (from-to)407-432
Number of pages26
JournalNonlinear Dynamics
Issue number1
StatePublished - Sep 27 2019

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