壓電致動器對混合邊界條件板結構之彎曲與振動分析

The deflection and vibration analysis of mixed boundary plate with piezoelectric actuators.

朱展緯(Jhan-Wei Jhu)

指導教授 ： 何旭川

元智大學/工程學院/機械工程學系/碩士(2006年)

https://doi.org/10.6838/YZU.2006.00066

摘要

本文探討壓電材料貼覆或內埋於混合邊界之平板，施予電壓對平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平板，同時施加大小相等、方向相反電壓，使平板產生彎曲變形。結合彈性力學與壓電原理推導壓電材料對平板所產生的作用力或力矩，再以此力或力矩為負載作用於平板，並應用板理論推導平板在不同邊界條件之撓曲位移與簡諧振動，再將推導所得解析解和有限元素數值解比較驗証。分析探討之混合邊界條件包含簡支撐、固定與自由邊等，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，再由改變電壓頻率了解共振與非共振頻率對平板之激振效果。

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 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 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 plate of mixed boundary condition 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 under mixed boundary condition are presented through parametric study. The response can be static or harmonic according to the static or sinusoidal voltage applied to the actuators. 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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