壓電致動器的動態與振動模擬分析

Dynamic Formulation and Vibration Analysis of the Piezoelectric Bending Actuators

黃友謙(Yu-Chien Huang)

指導教授 ： 黃健生

中原大學/工學院/機械工程研究所/碩士(2001年)

https://doi.org/10.6840/cycu200100036

摘要

本文主旨在分析兩種典型的壓電致動器：雙片壓電致動器（Bender-Bimorph Beam）以及單片壓電致動器（Bender-Unimorph Beam），分析兩者的動態模擬與其振動行為；考慮壓電致動器本身物理行為的壓電方程式，利用漢米頓原理（Hamilton’s principle）推導出完整的統御方程式，包含了動態方程式（Governing Equation）、連續方程式（Continuous Equation）、邊界條件（Boundary Condition）、以及轉換條件（Transition Condition）等等，比較兩種模型間的輸出效能與其相異處。利用有限元素法與程式的分析，在不同情況下做動態行為。在此並介紹利用壓電致動器應用於雷射偏光鏡（Optical Device）的例子。利用輸入電壓控制使鏡子達到要求的高度。在控制部份，利用虛擬根值法（Virtual Eigenvalue Method），結合傳統的線性回授控制以及變結構的切跳控制來達到模型減振的作用。

關鍵字

虛擬根植法 ； 雷射偏光器 ； 漢米頓原理 ； 壓電致動器

並列摘要

This paper investigates the dynamic formulations and vibration analyses of two typical piezoelectric bending actuators: the bender-unimorph and bender-bimorph beams. Dynamic equations of motion of the two typical models are completely derived by Hamilton’s principle. The differences and similarities between them are discussed where the dynamics and the efficiencies of the two typical models are investigated. The finite element method is employed to obtain dynamic responses with various conditions and to validate theoretic analysis. An example that the piezoelectric bender-bimorph beam is affixed with a mirror at its free end is designed for an optical device. Moreover, the virtual eigenvalue control method is employed to suppress vibrations of the optical device.

並列關鍵字

bimorph ； Hamilton principle ； piezoelectric actuators ； unimorph ； optical device

參考文獻

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