具有压电元件功能梯度弹性薄板的弯曲控制  

Bending Control of Functionally Gradient Thin Elastic Plate with Piezoelectric Patches Bonded

作　　者：刘玮[1] 丁丽霞[1] 

机构地区：[1]吉林大学数学学院,长春130012

出　　处：《吉林大学学报（理学版）》2008年第4期618-622,共5页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:10472037)

摘　　要：考虑一功能梯度薄板,其上下表面嵌有压电执行元件.假设梯度材料的弹性参数为板厚度方向坐标的幂函数,基于经典板理论,导出具有压电元件的功能梯度弹性薄板弯曲平衡微分方程.利用Navier和Levy解法得到在机、电载荷共同作用下一个四边简支矩形板的弯曲挠度.通过算例讨论了材料的梯度化、作用电压对板弯曲变形的影响.结果表明,材料的梯度化对弯曲变形有较大影响;而通过调整作用于执行元件上电压的大小和方向,可实现对板弯曲的有效控制.A hybrid rectangular plate comprised of a functionally graded materials substrate with piezoelectric patches perfectly bonded on its top and bottom surfaces as actuators was investigated. Based on the classical theory of plate, the equilibrium differential equation was deduced for the bending analysis of the thin elastic plate with functionally graded structure on the basis of assuming that functionally graded material properties obey a power law including thickness. The deflection was presented for a simply supported rectangular plate made of functionally graded material bonded piezoelectric patches subjected to electric-mechanical loading by means of Navier and Levy＇ s method. The numerical examples were given and the influences of functionally gradient exponent and applied voltage on the bending deflection were discussed. These results show that gradient exponent has an important effect on the bending deflection and the deflection can be controlled effectively by means of regulating the magnitude and direction of voltage applied on actuators.

关 键 词：弯曲控制 压电元件 功能梯度材料 弹性薄板 

分 类 号：O343.7[理学—固体力学]