Excitation of large-amplitude parametric resonance by the mechanical stiffness modulation of a microstructure

In this work we report on an approach allowing efficient parametric excitation of large-amplitude stable oscillations of a microstructure operated by a parallel-plate electrode, and present results of a theoretical and experimental investigation of the device. The frame-type structure, fabricated from a silicon on insulator (SOI) substrate using deep reactive ion etching (DRIE), consists a pair of cantilever-type suspensions connected at their ends by a link. The time-varying electrostatic force applied to the link by a parallel-plate electrode is transformed into a periodic tension of the beams, resulting in the modulation of their flexural stiffness and consequently the mechanical parametric excitation of the structure. The lateral compliance of the beams allows for large-amplitude in-plane oscillations in the direction parallel to the electrode while high axial stiffness prevents undesirable instabilities. The lumped model of the device, considered as an assembly of geometrically nonlinear massless flexures and a rigid massive link and built using the Rayleigh?Ritz method, predicted the feasibility of the excitation approach. The fabricated devices were operated in ambient air conditions by a combination of a steady (dc) and time-dependent (ac) components of voltage and the large-amplitude responses, up to 75 ?m, in the vicinity of the principal parametric and primary resonances were registered by means of video acquisition and image processing. The shapes of the experimental resonant curves were consistent with those predicted by the model. The location and size of the instability regions on the frequency?voltage plane (parametric tongues) were quantitatively in good agrement with the model results. Theoretical and experimental results indicate that the suggested approach can be efficiently used for excitation of various types of microdevices where stable resonant operation combined with robustness and large vibrational amplitudes are desirable.

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