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The design, modeling, fabrication, and characterization of a vibrationally trapped thickness-shear MEMS resonator is presented. This device is intended to avoid various limitations of flexural MEMS resonators, including nonlinearity, clamping losses, thermoelastic damping, and high damping in liquid. It includes a silicon bridge and a reference line on an SOI wafer, a coupled Au/Cr coplanar waveguide, Lorentz-force coupling, variations in waveguide thickness for vibrational trapping, and circuitry for nulling the components of the signal that are unrelated to the acoustic resonance. Finite-element vibrational modeling shows the lowest thickness-shear mode with a bridge thickness of 4.9 µm to be dominated by shear displacements, with the magnitude of out-of-plane displacements decreasing with increasing bridge width. Two-dimensional modeling of vibrational trapping, with central regions of the waveguides having 43 nm greater thickness, indicates that amplitudes are reduced by several orders of magnitude at the ends of the bridges for the fundamental ~ 400 MHz thickness-shear resonance. Sweptfrequency network-analyzer measurements of fabricated devices reveal no evidence for an acoustic resonance, despite a calculated prediction of levels of acoustic power absorption that are well above the measured noise level. A possible explanation for this result is stiction of the bridges to the substrate., Peer Reviewed, Postprint (published version)

The first objective of this dissertation is to present hybrid numerical-analytical approaches and reduced-order models to simulate microelectromechanical systems (MEMS) in multi-physics fields. These include electric actuation (AC and DC), squeeze-film damping, thermoelastic damping, and structural forces. The second objective is to investigate MEMS phenomena, such as squeeze-film damping and dynamic pull-in, and use the latter to design a novel RF-MEMS switch. In the first part of the dissertation, we introduce a new approach to the modeling and simulation of flexible microstructures under the coupled effects of squeeze-film damping, electrostatic actuation, and mechanical forces. The new approach utilizes the compressible Reynolds equation coupled with the equation governing the plate deflection. The model accounts for the slip condition of the flow at very low pressures. Perturbation methods are used to derive an analytical expression for the pressure distribution in terms of the structural mode shapes. This expression is substituted into the plate equation, which is solved in turn using a finite-element method for the structural mode shapes, the pressure distributions, the natural frequencies, and the quality factors. We apply the new approach to a variety of rectangular and circular plates and present the final expressions for the pressure distributions and quality factors. We extend the approach to microplates actuated by large electrostatic forces. For this case, we present a low-order model, which reduces significantly the cost of simulation. The model utilizes the nonlinear Euler-Bernoulli beam equation, the von K´arm´an plate equations, and the compressible Reynolds equation. The second topic of the dissertation is thermoelastic damping. We present a model and analytical expressions for thermoelastic damping in microplates. We solve the heat equation for the thermal flux across the microplate, in terms of the structural mode shapes, and hence decouple the