An Analytical Solution to the Pull-in Voltage of the Micro Curled Cantilever Beam subjected to Electrostatic Load and Its Application to Extract the Young’s Modulus and Stress Gradient of Thin Films
碩士 === 國立臺灣科技大學 === 機械工程系 === 95 === ABSTRACT The analytical modeling of the electrostatic devices is quite complicated and difficult in virtue of such effects as the electric-mechanical coupling effect, the nonlinearity of the electrostatic force, the fringe field, and the pre-deformation of the mi...
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| Format: | Others |
| Language: | zh-TW |
| Published: |
2007
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| Online Access: | http://ndltd.ncl.edu.tw/handle/18803571709271847805 |
| Summary: | 碩士 === 國立臺灣科技大學 === 機械工程系 === 95 === ABSTRACT
The analytical modeling of the electrostatic devices is quite complicated and difficult in virtue of such effects as 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 aims at developing an analytical solution to the pull-in voltage of a micro curled cantilever beam subjected to electrostatic loads. High precision analytical solution to the pull-in voltage and its application to extract the young’s modulus and stress gradient of thin films is established in this thesis.
First of all, we use energy method to drive out the bending strain energy and fringing field effect electrical potential energy of the micro curled beam subjected to electrostatic loads. Continuously, the analytical solution to the pull-in voltage is derived based on the minimum energy method and assumed deflection shape function. Then one can use the aforesaid analytical solution of the pull-in voltage to extracted the Young’s modulus and stress gradient of the test structures. The accuracy and precision of the present method for extracting the Young’s modulus and residual stress is verified through comparing with the results conducted in the published works as well as the experiment conducted by the author. The error of the extracted Young’s modulus and stress gradient are below 2% compared to the experimentally measured data.
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