| Summary: | 博士 === 國立臺灣大學 === 工程科學及海洋工程學研究所 === 101 === The dynamics and stabilities of a micro-beam subjected to a to and fro traveling electrostatic force were investigated in this thesis. Research topics include the dynamics of a micro-beam subjected to a traveling load, the dynamics and stabilities of a micro-beam subjected to and fro traveling electrostatic loads.
In this study, Hamilton principle is first used to derive the nonlinear partial differential equation with the nonlinear electrostatic term. The position of the electrostatic load defined as Dirac delta function. Expand the electrostatic term by the Taylor series expansion. Based on the small deflection assumption, the second and higher order terms of the electrostatic expansion can be neglected, get a linearized equations of motion for the structure and electrostatic coupling effect, and finally the use of the mode expansion method yields the discrete equation of motion, then the dynamics of a micro-beam subjected to a to and fro traveling electrostatic force were investigated
In the numerical analysis, Runge-Kutta Method is used to find dynamic responses. According to the analytical results, the resonant frequencies of a structure will be bifurcated by the traveling harmonic loads. Apart from Floquet’s theory, the beam may be unstable at some unstable traveling speeds. Furthermore the unstable regions expand with increasing driving voltage.
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