壓電致動器對板結構之彎曲與振動分析

The Deflection and Vibration Analysis of A Simply Supported Plate with Piezoelectric Actuators

劉俊彥(Chun-Yen Liu)

指導教授 ： 何旭川

元智大學/工程學院/機械工程學系/碩士(2003年)

摘要

本文探討壓電材料貼覆或內埋於平板，施予電壓對平板產生的靜態撓曲變形和簡諧振動。結合彈性力學理論與壓電原理推導壓電材料和平板接觸面作用力或力矩，再以此力或力矩為負載作用於平板，應用板理論求解平板撓曲位移或簡諧振動。並以簡支撐平板為例，比較推導所得解析解和有限元素數值解兩者相當吻合，驗證推導的準確性。藉由參數分析探討壓電片大小及放置位置之影響，表面貼覆與內埋之差異，再由改變施予之電壓頻率了解共振與非共振頻率對平板之激振效果。壓電材料為智慧結構常見的感測和致動元件，本文推導所得可作為此類型智慧結構分析的理論基礎。

關鍵字

壓電材料 ； 板理論 ； 撓曲位移 ； 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 actuator ； classical plate theory ； harmonic vibration ； smart structure

參考文獻

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