Microplates are the building blocks of many micro-electro-mechanical systems. It is common for them to experience initial curvature imperfection due to residual stresses caused by the micro fabrication process. Such plates are essentially different from perfectly flat ones and cannot be modeled using flat plate models. In this paper, we adopt a dynamic analog of the von Karman governing equations of imperfect plates. These equations are then used to develop a reduced order model based on the Galerkin procedure, to simulate the static and dynamic behavior of the microplate under electrostatic actuation. To validate the simulation results, an initially curved imperfect microplate made of silicon nitride is fabricated and tested. The static behaviour of the microplate is investigated when applying a DC voltage V dc . Then, the dynamic behaviour of the microplate is examined under the application of a harmonic AC voltage, V ac , superimposed to V dc . The simulation results show good agreement with the experimentally measured responses.

We present an experimental investigation for the nonlinear dynamic behaviors of clampedclamped in-plane MEMS shallow arches when excited by harmonic electrostatic forces. Frequency sweeps are conducted to study the dynamic behaviors in the neighborhoods of the first and third resonance frequencies as well as the super-harmonic resonances. Experimental results show local softening behavior of small oscillations around the first resonance frequency and hardening behavior at the third resonance frequency for small dc and ac loads. Interesting dynamic snap-through cross-well motions are observed experimentally at high voltages for the first time in the micro-scale world. In addition to the dynamic snap-through motion, the MEMS arch exhibits large oscillations of a continuous band of snap-through motion between the super-harmonic resonance regime and the first primary resonance regime. This continuous band is unprecedented experimentally in the micro/macro world, and is promising for a variety of sensing, actuation and communications applications.

This paper presents an experimental study and a finite-element analysis of the effect of squeeze film damping on the resonance frequency and quality factor of the higher-order flexure vibrations modes of clamped–clamped microbeams. Viscoelastic and silicon nitride microbeams are fabricated and are electrostatically actuated by various electrode configurations to trigger the first, second, and third modes. The damping characteristic and the resonance frequency of these modes are examined for a wide range of gas pressure and electrostatic voltage loads. The results of the silicon nitride beams and viscoelastic beams are compared. It is found that the intrinsic material loss is the major dissipation mechanism at low pressure for the viscoelastic microbeams, significantly limiting their quality factor. It is also found that while the silicon nitride beams show higher quality factors at the intrinsic and molecular regimes of pressure, due to their low intrinsic loss, their quality factors near atmospheric pressure are lower than those of the viscoelastic microbeams. Further, the higher-order modes of all the beams show much higher quality factors at atmospheric pressure compared to the first mode, which could be promising for operating such resonators in air. Experimental results and finite element model simulations show good agreement for resonance frequency and quality factor for the three studied modes.

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