壓電致動器對混合邊界條件複合材料層板結構之彎曲與振動分析

The Deflection and Vibration Analysis of Laminated Plate Induced By Piezoelectric Actuators Under Mixed Boundary Condition

呂俊慶(Chun-Ching Lu)

指導教授 ： 何旭川

元智大學/工程學院/機械工程學系/碩士(2008年)

https://doi.org/10.6838/YZU.2008.00262

摘要

本文探討壓電材料貼覆或內埋於混合邊界之複材層板，施予電壓對複材層板所產生的靜態撓曲變形和簡諧振動振幅。將兩片壓電片以上下對稱方式貼覆或內埋於複材層板，同時施加大小相等、方向相反電壓，使複材層板產生彎曲變形。結合彈性力學與壓電原理推導壓電材料對複材層板所產生的作用力或力矩，再以此力或力矩為負載作用於複材層板，邊界條件為左右兩邊簡支撐上下兩邊固定。應用疊加原理與Levy’s方法求解簡支撐與固定支撐混合邊界條件複材層板撓曲變形與簡諧振動，並與三維有限元素分析數值解比較，驗證理論推導的準確性。探討改變壓電片尺寸與放置位置之影響，比較表面貼覆與內埋之差異，並藉由改變電壓頻率了解共振與非共振頻率對複材層板之激振效果。
關鍵字：壓電材料、Levy’s方法、簡諧振動、混合邊界條件

關鍵字

壓電材料 ； Levy’s方法 ； 簡諧振動 ； 混合邊界條件

並列摘要

In this investigation, the static deflection and harmonic vibration of laminated plate induced by piezoelectric actuators under mixed boundary condition are examined. Two piezoelectric actuators are surface bonded or embedded in the plate and are symmetric with the mid-plane. Electric voltages with the same amplitude and opposite sign are applied to the two symmetric piezoelectric actuators, results to the bending effect on the laminated plate. The bending moment is derived by using the theories of elasticity and piezoelectricity. This bending moment is then applied to the laminated plate. The laminated plate is simply supported along the left and right edges, and fixed along the top and bottom edges. The principle of superposition and Levy’s solution are employed to solve the static doformation and harmonic vibration of the laminated plate with mixed boundary condition.The analytical solutions are compared with the three dimentional finite element results to show the accuracy of present approach. The effects of size and location of actuators on the response of the laminated plate under mixed boundary condition are presented through parametric study. The analytical model presented in this research demonstrates the capability of predicting the responses of smart structures to a command voltage applied to the piezoelectric actuators.

Keyword ：piezoelectric actuator, Levy’s solution, harmonic vibration, mixed boundary condition

並列關鍵字

piezoelectric actuator ； Levy’s solution ； harmonic vibration ； mixed boundary condition

參考文獻

[2] 林琪昇, 「壓電致動器對複合材料層板結構之彎曲與振動分析」,私立元智大學,碩士論文,民國93年。

[4] E.F. Crawley and J.de. Luis, Use of piezoelectric actuators as element of intelligent structures, AIAA Journal, 25(1987), 1373-1385.

[5] E.K. Dimitriadis, C.R. Fuller and C.A. Roger, Piezoelectric actuators for distributed vibration excitation of thin plate, Journal Vibrat Acoust, 13(1991), 100-7.

[6] J.N.Reedy, Mechanics of laminated composite plates and shells theory and analysis,CRC PRESS (2004).

[7] Carl T. Herakovich ,Mechanics of fibrous composites ,John Wiley & Sons ,Inc (1998).