壓電複合樑之諧振特性分析

Transverse Vibration Analysis for Piezoelectric Composite Beams in Resonance

王鵬凱(Peng-Kai Wang)

指導教授 ： 黃吉宏

健行科技大學/工學院/機械工程所/碩士(2012年)

摘要

本文主要藉由一維古典樑理論與壓電力學理論，以求出雙層複合壓電樑在單邊固定邊界條件下之伸展及側向振動特性。主要利用應變與位移關係式、電場與電位關係式及相關組成關係式，推導出該振動模式下之統御方程式，最後運用拉氏轉換得到共振頻率之特徵方程式。為了驗證理論計算之正確性，本文利用有限元素法(FEM)從事數值計算，以獲得其共振頻率與振型，並將兩者結果作一系列之比較。本文也針對多種不同長寬比及不同厚度比之雙層複合壓電樑進行理論預測，以探討伸展及側向模態振頻與不同幾何變化間之關係。

關鍵字

側向振動 ； 伸展震動 ； 壓電陶瓷 ； 壓電樑

並列摘要

The dissertation employs the one-dimensional classical beam theory and piezoelectric mechanics theory to investigate the extensional vibration and transverse vibration for bilayered piezoelectric composite beams with cantilever boundary conditions. In this dissertation, the governing equations of vibration modes were carefully derived by strain-displacement relation and the electric field-potential relation. Then the Laplace transform were used to obtain the characteristic function of resonant frequencies. The numerical calculations obtained by finite element method (FEM) is carried out to validate the theoretical analysis and good agreements are obtained. With reference to the different thickness ratios and aspect ratios, the vibration characteristics of cantilever piezoelectric composite beams are discussed in details.

並列關鍵字

transverse vibration ； extensional vibration ； piezoceramic ； piezoelectric composite beams

參考文獻

[1]吳建鋒，「壓電感測器及致動器之分析」，私立逢甲大學，機械工程研究所碩士論文，民國八十九年。

[2]林憲陽，「壓電陶瓷負荷曾板動態特性之數值分析與實驗量測」，國立台灣大學，機械工程研究所博士論文，民國九十一年。

[3]Adelman, N. T. and Stavsky, Y., “Axisymmetric Vibration of Radially Polarized Piezoelectric Ceramic Cylinders”, Journal of Sound and Vibration, 38(2), pp. 245-254, 1975.

[4]Adelman, N.T. and Stavsky, Y., “Vibration of Radially Polarized Composite PiezoelectricCylinders and Disks”, Journal of Sound and Vibration, 43(1), pp. 37-44, 1975.

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