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Two-To-One Internal Resonance in Microscanners

M.F. Daqaq, E.M. Abdel-Rahman and A.H. Nayfeh
Virginia Polytechnic Institute and State University, US

Keywords:
micromirrors, internal resonance, reduced-order model

Abstract:
In micoscanning, micromirrors are excited at their resonance frequency to achieve large scanning angles, while minimizing the voltage requirements. In this work, we derived a reduced-order model by applying a Galerkin expansion to the distrubuted-parameter system of the mirror. The free vibration problem indicates that the natural frequencies of the higher modes are two orders of magnitude larger than the first two natural frequencies corresponding to the first torsion and bending modes of the suspension beams. Therefore, under normal operating conditions, the mirror will respond only in the first two modes, which justifies the use of a 2-DOF lumped-mass model.
 
Within a certain DC voltage range, a two-to-one internal resonance occurs between the first two modes, causing energy exchange between the modes. This results in undesirable fluctuations in the tilt angle. The present analysis allows mirror designers to identify and design around this phenomenon as well as apply control strategies to alleviate it.

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