受電負載的微型樑之非線性振動之研究

A Study of Nonlinear Vibration of a Microbeam to an Electric load

張原銘(Yun-Ming Chang)

指導教授 ： 施延欣

中原大學/工學院/機械工程研究所/碩士(2010年)

https://doi.org/10.6840/CYCU.2010.00020

摘要

中文摘要

本文是探討兩端為固定的微樑，由電力驅動負載組成的極化電壓的DC組件與AC組件。並且在這個微樑結構中考慮粘性阻尼的影響。然後就非線性自然頻率與線性自然頻率的比值，無因次化係數的軸向力進行研究。分析中，使用漢彌爾頓理論推導出微樑的運動方程式，設計參數都包含在模型內歸併成無綱量參數，再經過Gslerkin's方法，將微樑的運動方程式轉換成具時間係數的Mathieu方程式。本文中，不同值的驅動電壓(Vac)、軸向力對於振動頻率比(frequency ratio)的影響；該模型在擾動分析下得到的結果進行比較，驗證它們與已發表的理論與實驗結果。

關鍵字

諧振器 ； 微機電系統 ； 強迫振動 ； 主共振

並列摘要

Abstract

This study investigates the micro-beam, which the both ends are fixed, and actuated by the electric load composed of the polarization voltage DC component and the AC components. The viscous damping is considered in this microbeam structure. The nonlinear and linear natural frequency ratio, and dimensionless coefficient of the axial force are considered. The governing equation of motion is theoretically derived using Hamilton's principle, the design parameters are included in the model parameters merge into nondimensional parameters. Applying Gslerkin's method to simplify the governing equation of motion into Mathieu equation with time-dependent coefficients. In this study, driving voltage, the axial force influence on the vibration frequency ratio (frequency ratio); In this analysis, the results are verified with the published theoretical and experimental results.

並列關鍵字

forced vibration ； primary resonance ； MEMS ； resonator

參考文獻

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