受電負載的微型樑之大振幅振動分析

Large Amplitude Vibration of a Microbeam with Electric Load

林軒竹(Hsuan-Chu Lin)

指導教授 ： 施延欣

中原大學/工學院/機械工程研究所/碩士(2012年)

https://doi.org/10.6840/cycu201201003

摘要

本文為探討兩端固定之微型樑，藉由電力驅動負載組成的極化電壓之DC組件以及AC組件。並且在這個微型樑結構當中考慮粘性阻尼造成的影響。之後就非線性自然振動頻率與線性自然振動頻率的比值，利用無因次化的軸向力進行振動研究。在分析當中，使用漢彌爾頓理論推導出微型樑的運動方程式，設計參數皆包含在模型內歸併成無因次參數，在經過Galerkin’s方法，將微型樑的運動方程式轉換成為具有時間變數的方程式。接下來，討論不同的電壓(Vac)、振幅對於振動頻率比(Frequency ratio)的影響，與該模型在微擾分析下得到的結果進行比較，驗證本文與已發表的理論以及實驗結果。並且使用不同振幅來觀察其振動的模式。

關鍵字

諧振器 ； 主共振 ； 微機電系統 ； 強迫振動

並列摘要

In this study, we discuss the microbeam which are fixed in both ends, and use electric loading of the polarization voltage DC component and the AC component to actuated it. The viscous damping is considered in this microbeam structure. Then calculate the nonlinear natural frequency ratio , linear natural frequency ratio and dimensionless coefficient of the axial force to analyze. By using Hamilton's principle to derived the governing equation of motion , the parameters of influence are included in the model, then merge parameters into non dimensional parameters. After applying Galerkin's method, governing equation of motion is simplified into Mathieu equation with time variable. Finally the effect of the driving voltage and the amplitude on the frequency ratio is discussed and verified the results with the published theoretical and experimental results, then observe the pattern of vibration .

並列關鍵字

MEMS ； resonator ； primary resonance ； forced vibration

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