Abstract
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.
Highlights
Energy transfer via internal resonance among various modes of vibration of micro and nano-electromechanical structures (MEMS and NEMS) has been explored for several potential applications, such as timing/synchronization [1,2], energy harvesting [3,4], mass sensing [5], and frequency stabilization [6,7]
One should note that the partial electrode electrostatic actuation breaks the symmetry of forcing causing hybridization of the first symmetric and antisymmetric modes of the arch beam near crossing where the 1:1 and 2:1 internal resonances are observed [A
The dynamic response is measured by sweeping the excitation frequency for various DC and AC electrostatic loads
Summary
Energy transfer via internal resonance among various modes of vibration of micro and nano-electromechanical structures (MEMS and NEMS) has been explored for several potential applications, such as timing/synchronization [1,2], energy harvesting [3,4], mass sensing [5], and frequency stabilization [6,7].
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