| Summary: | 碩士 === 國立臺灣科技大學 === 機械工程系 === 93 === The analytical modeling of the electrostatic devices is quite complicated and difficult in virtue of the electric-mechanical coupling effect, the nonlinearity of the electrostatic force, the fringe field, and the pre-deformation of the micro-structure caused by the residual stress and stress gradient. This thesis is to investigate the pull-in phenomenon of the pre-deformed microstructures subjected to electrostatic loads. High precision analytical modeling of the threshold voltage is established in this thesis.
First of all, we use energy method to drive out the bending strain energy and electrical potential energy of the micro curled beam subjected to electrostatic loads. Based on the assumption of small deflection and adopting the Taylor series expansion, the expression of the total potential energy can be simplified as third-order and fourth-order models by omitting the terms with higher order than the third-order and the fourth-order respectively. Continuously, by the use of Rayleigh-Ritz method and assumed mode method, the approximate analytical solutions of the threshold voltage of curled beams are obtained based on the full-order, the third-order, and the fourth-order models respectively. The results obtained by this work agree more well to the experimental results compared to the published works. Five common used assumed deflection shape functions, including the natural mode, the uniform load deflection function, the concentrated load deflection function, the combined loads deflection function, and the square function are also compared with each other. The natural mode is verified to be the best choice. The numerical results show that the greatest error of the full-order model is below 8%, the one of the fourth-order model is below 9%, the one of the third-order model is below 18%, and the one of the literature is below 37%.
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