壓電致動器對複合材料層板結構之彎曲與振動分析

THE DEFLECTION AND VIBRATION ANALYSIS OF A SIMPLY SUPPORTED LAMINATE PLATE WITH PIEZOELECTRIC ACTUATORS

林琪昇(Chi-Sheng Lin)

指導教授 ： 何旭川

元智大學/工程學院/機械工程學系/碩士(2004年)

摘要

本文探討壓電材料貼覆或內埋於複材層板之靜態變形與動態振動振幅，複材層板疊層為[0/90]屬Cross-ply，邊界條件為四邊簡支撐。將兩片壓電片以對稱方式貼覆或內埋於複材層板上，同時施加大小相同方向相反電壓，可為固定電壓或固定頻率及振幅之正弦函數，結合壓電效應、複合材料層板理論及板殼原理，推導壓電材料與主結構之變形傳遞關係，探討複材層板在靜態與簡諧振動響應。藉由改變壓電片尺寸及放置位置之影響，表面貼覆與內埋之差異，再由改變施加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 ； 板殼理論 ； 複合材料層板理論 ； 簡諧振動

並列摘要

In this investigation, the static deflection and harmonic vibration of a simply supported plate induced by piezoelectric actuators are examined two piezoelectric actuators are surface bonded or embedded in the plate and are symmetric with the mid-plane. Electric voltage with the same amplitude and opposite sign are applied to the two symmetric piezoelectric actuators, results to the bending effect on the plate. The bending moment is derived by using the theories of elasticity and piezoelectricity. This bending moment is then applied to the plate. Following the classical plate theory, the analytical solution of flexural displacement on a simply supported plate subjected to bending moment can be obtained. The analytical solution are compared with the finite element results to show the validation of present approach. The effects of size and location of actuators on the response of a plate are presented through parametric study. The response can be static or harmonic according to the static or sinusoidal voltage applied to the actuators. Piezoelectric actuators are common used in smart structures. 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.

並列關鍵字

piezoelectric actuators ； classical plate theory ； harmonic vibration

參考文獻

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