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研究生： 郭家成
Chia-chen Kuo
論文名稱： 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
指導教授： 黃以玫
Yi-mei Huang
口試委員:
學位類別： 碩士
Master
系所名稱： 工學院 - 機械工程學系
Department of Mechanical Engineering
論文出版年： 2014
畢業學年度： 102
語文別： 中文
論文頁數： 101
中文關鍵詞： 壓電吸振器 、懸臂樑 、狀態變換 、振動控制
外文關鍵詞： vibration control, cantilever beam, state-switched, piezoelectric absorber
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    • 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。

    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.

    中文摘要 i 英文摘要 ii 致謝 iii 目錄 iv 圖目錄 vii 表目錄 xii 符號說明 xiii 第一章 緒論 1 1-1 前言 1 1-2 研究動機 1 1-3 文獻回顧 2 1-4 內容架構 4 第二章 壓電材料理論 5 2-1 壓電材料簡介 5 2-2 壓電現象 6 2-3 壓電材料方程式 7 第三章 複合運動系統方程式 10 3-1 方程式基本假設 10 3-2 漢米頓原理 11 3-3 系統運動方程式 14 3-4 系統運動方程式離散化 16 第四章 吸振電路方程式 19 4-1 壓電材料電壓轉換 19 4-2 標準式被動吸振器 20 4-2-1 標準式被動吸振電路方程式 20 4-2-2 標準式被動吸振器與系統近似解 22 4-3 半主動式狀態變換壓電吸振器 23 4-3-1 半主動式狀態變換吸振電路方程式 23 4-3-2 半主動式狀態變換吸振器與系統近似解 25 第五章 半主動式狀態變換吸振器之數值結果與分析 29 5-1 數值程式架構 29 5-2 系統參數設定 30 5-3 標準式被動吸振器數值分析 31 5-4 半主動式狀態變換吸振器數值結果分析 32 5-4-1 設計一半主動式狀態變換吸振器數值結果分析 32 5-4-2 設計二半主動式狀態變換吸振器數值結果分析 34 5-4-3 設計三半主動式狀態變換吸振器數值結果分析 36 5-4-4 設計四半主動式狀態變換吸振器數值結果分析 38 第六章 半主動式狀態變換吸振器實驗結果 42 6-1 實驗設備和實驗流程介紹 42 6-2 實驗結果分析 43 6-2-1 被動式吸振器實驗結果分析 43 6-2-2 半主動式狀態變換吸振器時節結果分析 44 6-3 數值模擬與實驗結果分析 45 第七章 結論與未來建議 48 7-1 結論 48 7-2 未來建議 49 參考文獻 51

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