電縮複合積層板的致動機電響應

The Electro-Mechanical Response of Electrostrictive Composite Laminates Due to Actuation

張原銘(Yuan-Ming Chang)

指導教授 ： 余念一

元智大學/工程學院/機械工程學系/碩士(2004年)

摘要

古典積層板理論在本研究中被延伸來探討智慧型電縮(或譯電歪)複合材料的非線性機電耦合現象。我們採用兩種求解方法去預測積層板遭受到電場作用時，其各層的應力和應變。第一種方法為解析解，它忽略本構方程中的一高階非線性耦合項，此解析解當作第二種數值解的初始值,以逼近求解。數值解考慮較完整的本構方程式，結果兩種方法所求得的結果十分逼近,證明了本構方程中的該高階非線性耦合項的影響微乎其微。我們所考慮的材料是等向性的電縮弛豫鐵電體鈮鎂酸鉛陶瓷(lead magnesium niobate, PMN)，搭配黃銅、鋁或是環氧樹脂堆疊成各種不同的複合積層板，結果顯示當遭受到一電場作用，不同材料性質的效應，也探討不同厚度跟層數的對電縮複合材料的影響。最後，極化飽和對電縮複材致動響應的影響也詳加討論。

關鍵字

電縮 ； 積層板 ； 壓電 ； 致動 ； 機電耦合

並列摘要

The classical laminated plate theory (CLPT) is extended to study the nonlinear electro-mechanical coupling in smart electrostrictive composite materials. Both numerical and analytic solutions are obtained to predict the in-plane strains and stresses of electrostrictive laminated composites subjected to through-the-thickness electric fields. The analytic solutions are obtained by ignoring a higher-order nonlinear term in the constitutive relations of electrostrictive materials. The analytic solutions can be used as the initial solutions of a numerical scheme. Both the numerical and the analytic solutions give almost identical solutions, which shows that the higher-order nonlinear term in the constitutive relation of electrostrictive materials is negligible.
Three ductile materials ─ brass, aluminum, and epoxy ─ are combined with lead magnesium niobate(PMN). The effects of material properties and geometry (number of plies, ply thickness, etc.) on the electrical and mechanical response of electrostrictive laminated composites are examined. Finally, the effects of saturation of polarization on the electro-mechanical response of electrostrictive laminated composites due to actuation is studied.

並列關鍵字

electrostrictive ； laminates ； piezoelectric ； actuation ； electro-mechanical coupling

參考文獻

Chou, T. W. (1992), Microstructural Design of Fiber Composites, Cambridge.

Damjanovic, D. and Newnham, R. E. (1992), “Electrostrictive and Piezoelectric Materials for Actuator Application,” Journal of Intelligent Material Systems and Structures, 3, pp. 190-208.

Daniel, I. M. and Ishai, O. (1994), Engineering Mechanics of Composite Materials, Oxford.

Hom, C. L. and Shankar, N. (1994), “A Fully Coupled Constitutive Model for Electrostrictive Ceramic Materials,” Journal of Intelligent Material Systems and Structures, 5, pp. 795-801.

Ikeda, T. (1990), Fundamentals of Piezoelectricity, Oxford Science Publications.