被動式狀態變換壓電吸振器應用於懸臂樑之減振

Reducing Vibration of a Cantilever Beam By Passive State-Switched Piezoelectric Absorbers

郭家成(Chia-chen Kuo)

指導教授 ： 黃以玫

國立中央大學/工學院/機械工程學系/碩士(2014年)

摘要

本文主要目的為探討半主動式狀態變換壓電吸振器，應用於受外力作用而產生振動之懸臂樑，在懸臂樑表面貼附成對陶瓷壓電材料，外接一組由電阻、電感、二極體所組成之吸振電路，模擬類似機械式吸振器之吸振電路，並藉由二極體的限制電流方向之特性，電流分流之間的切換達到電路狀態變換的效果，即二極體之被動式控制取代由速度或位移回饋訊號之狀態變換吸振電路。
內容包含被動式電路和半主動式狀態變換電路之減振效果分析，首先從漢米爾頓原理推導懸臂樑結構方程式與自然頻率，接著推導狀態變換吸振電路方程式，並將結構方程式與電路方程式進行耦合，使用數值程式求解聯立常微分方程式，求得系統之位移響應與電路中參數響應。透過不同型態電路設計與電路參數調整，研究出較佳的半主動式狀態變換吸振電路設計，接著透過實驗驗證數值模擬分析之結果，歸納出合適設計之半主動式狀態變換吸振器。

關鍵字

壓電吸振器 ； 懸臂樑 ； 狀態變換 ； 振動控制

並列摘要

The purpose of this research is to reduce the vibration of a cantilever beam by using state-switched piezoelectric absorbers. Two pieces of piezoelectric materials are attached to both sides of a cantilever beam. A state-switched absorbers consists of piezoelectric sheet, inductance, resistance, voltage source and a diode. The conducting state of diode determines the switching of circuit.
Content of the thesis includes vibration reduction analysis of passive and state-switched absorbers. The equations of motion of the beam are derived by Hamilton’s principle and discretized by Galerkin’s method. Numerical program simultaneously solves the equations of motion of the beam and circuit equation of the absorber. Both of numerical and experimental results conclude effective designs of state-switched absorbers.

並列關鍵字

vibration control ； cantilever beam ； state-switched ； piezoelectric absorber

參考文獻

許校瑋, 2011, “壓電式碰撞吸振器之減振機制”, 國立中央大學機械工程研究所碩士論文, 桃園縣

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Corr, L.R. and Clark, W.W., 2002, “Comparison of low-frequency piezoelectric switching shunt techniques for structural damping,” Smart Materials and Structures, Vol. 11, pp. 370–376.

Corr, L.R. and Clark, W.W., 2003, “A Novel Semi-Active Multi-Modal Vibration Control Law for a Piezoceramic Actuator,” ASME Journal of Vibration and Acoustics, Vol. 125, pp. 241-222.