| Summary: | 碩士 === 國立交通大學 === 電機與控制工程系所 === 95 === This study is devoted to provide precise predictions of the static and dynamic pull-in voltage of a general clamped-clamped micro-beam based on a continuous model. The pull-in is a phenomenon which occurs when the electrostatic force on the micro-beam exceeds the elastic restoring exerted by beam deformation, leading to a contact between the actuated beam and the bottom electrode. To derive pull-in voltage, a dynamic model in partial differential equations is established based on the equilibrium among beam flexibility, inertia, residual stress, squeeze film, distributed electrostatic forces and its electrical field fringing effects. The method of Galerkin decomposition is next employed to convert the established system partial differential equations into reduced discrete modal equations. Considering lower-order modes and approximating the deflection by a different order series, the bifurcation based on phase portraits are conducted to derive static and dynamic pull-in voltages. It is found that the pull-in phenomenon follows well a known generalized homoclinic bifurcation, and the dynamic pull-in voltage is around 91 to 92 % of the static counterpart. However, the derived dynamic pull-in voltage is found dependent on the varied beam parameters, different from a fixed predicted value derived in past works, where only lumped models are assumed. Furthermore, accurate closed-form predictions are provided for the cases of non-narrow beams. The predictions are finally validated by finite element analysis and existing experimental data.
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