Gas damping of electrostatically excited resonators

Corman, Thierry; Enoksson, Peter; Stemme, G.

doi:10.1016/s0924-4247(97)80270-1

Cited by 46 publications

(33 citation statements)

References 10 publications

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“…For a cantilever beam, the nth natural resonant frequency of vibration ω n is given by its characteristic function where γ n are 1.8751, 4.9641 and 7.8548 for the first three modes of fixed-free cantilevers, and are 4.7300, 7.8532 and 10.9956 for the first three modes of fixed-fixed (clamped) beams. As shown in equation (1), the quality factor, Q n , increases proportionally with the resonant frequency, ω n , for the same damping force c f .…”

Section: Gas Damping Modelsmentioning

confidence: 96%

Compact model of squeeze-film damping based on rarefied flow simulations

Guo

Alexeenko

2009

J. Micromech. Microeng.

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A new compact model of squeeze-film damping is developed based on the numerical solution of the Boltzmann kinetic equation. It provides a simple expression for the damping coefficient and the quality factor valid through the slip, transitional and free-molecular regimes. In this work, we have applied statistical analysis to the current model using the chi-squared test. The damping predictions are compared with both Reynolds equation-based models and experimental data. At high Knudsen numbers, the structural damping dominates the gas squeeze-film damping. When the structural damping is subtracted from the measured total damping force, good agreement is found between the model predictions and the experimental data.

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Section: Gas Damping Modelsmentioning

confidence: 96%

Compact model of squeeze-film damping based on rarefied flow simulations

Guo

Alexeenko

2009

J. Micromech. Microeng.

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“…[4][5][6] In particular, the modeling of squeeze-film damping (SFD) of microstructures at a wide range of pressures is challenging due to the breakdown of conventional fluid dynamic models in the rarefied flow regime. The squeeze-film damping force is generated due to a small pressure difference between the top and bottom surfaces of a moving structure .…”

Section: -3mentioning

confidence: 99%

Simulations of Aerodynamic Damping for MEMS Resonators

Guo

Alexeenko

2009

39th AIAA Fluid Dynamics Conference

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Aerodynamic damping for MEMS resonators is studied based on the numerical solution of Boltzmann-ESBGK equation. A compact model is then developed based on numerical simulations for a wide range of Knudsen numbers. The damping predictions are compared with both Reynold equation based models and several sets of experimental data. It has been found that the structural damping is dominant at low pressures (high Knudsen numbers). For cases with small length-to-width ratios and large vibration amplitudes, the threedimensionality effects must be taken into account. Finally, an uncertainty quantification approach based on the probability transformation method has been applied to assess the influence of pressure and geometric uncertainties. The output probability density functions (PDF) of the damping ratio has been studied for various input PDF of beam geometry and ambient pressure.

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“…Note that the inertial nonlinearities due to in-plane rotation of the pedal about Z axis, terms with Γ , also result in mistuning the flexural mode natural frequency due to the nontrivial equilibrium position. The parameters ω 1 , ω 2 , R 1 , and R 2 in (28) and (29), and when used later in this section, are evaluated at the nominal dimensions () c .…”

Section: Averaged Equationsmentioning

confidence: 99%

Dynamics of a nonlinear microresonator based on resonantly interacting flexural-torsional modes

2008

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A novel microresonator operating on the principle of nonlinear modal interactions due to autoparametric 1:2 internal resonance is introduced. Specifically, an electrostatically actuated pedal-microresonator design, utilizing internal resonance between an out-of-plane torsional mode and a flexural in-plane vibrating mode is considered. The two modes have their natural frequencies in 1:2 ratio, and the design ensures that the higher frequency flexural mode excites the lower frequency torsional mode in an autoparametric way. A Lagrangian formulation is used to develop the dynamic model of the system. The dynamics of the system is modeled by a two degrees of freedom reduced-order model that retains the essential quadratic inertial nonlinearities coupling the two modes. Retention of higher-order model for electrostatic forces allows for the study of static equilibrium positions and static pull-in phenomenon as a function of the bias voltages. Then for the case when the higher frequency flexural mode is resonantly actuated by a harmonically varying AC voltage, a comprehensive study of the response of the microresonator is presented and the effects of damping, and mass and structural perturbations from nominal design specifications are considered. Results show that for excitation levels above a threshold, the torsional mode is activated and it oscillates at half the frequency of excitation. This unique feature of the microresonator makes it an excellent candidate for a filter as well as a mixer in RF MEMS devices.

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Gas damping of electrostatically excited resonators

Cited by 46 publications

References 10 publications

Compact model of squeeze-film damping based on rarefied flow simulations

Compact model of squeeze-film damping based on rarefied flow simulations

Simulations of Aerodynamic Damping for MEMS Resonators

Dynamics of a nonlinear microresonator based on resonantly interacting flexural-torsional modes

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