带压电层功能梯度悬臂板非线性动力学分析  

Nonlinear dynamics of a functionally graded rectangular cantilever plate with piezoelectric

作　　者：郝育新[1] 孙彦军[1] 王建华[1] 

机构地区：[1]北京信息科技大学机电工程学院,北京100192

出　　处：《北京信息科技大学学报（自然科学版）》2010年第3期19-24,共6页Journal of Beijing Information Science and Technology University

基　　金：国家自然科学基金(10972026);北京市教育委员会科技计划面上项目(KM200910772004和KM201010772003);北京市属高等学校人才强教计划资助项目(PHR200906213);2010年科研水平提高项目(5028123103)

摘　　要：分析了在热环境条件下受横向载荷作用的、带压电功能梯度材料悬臂板的非线性动力学问题。基于von Karman理论和Reddy一阶剪切变形理论,推导出了带压电功能梯度悬臂板的动力学方程。利用Galerkin法对偏微分方程进行离散,对离散后的方程进行数值模拟,分析中考虑了组分材料热物参数对温度变化的依赖性,讨论了材料组分指数、控制电压对系统非线性动力学行为的影响,结果表明正电压减小了板的振幅,负电压增大了板的振幅,而随着材料体积分数指数的增大,板的振幅也在变大。The nonlinear dynamics of a functionally graded rectangular cantilever plate with piezoelectric subjected to transverse loads in thermal environments is investigated in this paper. The governing equations of the functionally graded plate are based on yon Karman theory and Reddy＇ s first-order shear deformation plate theory that includes thermal effects. Galerkin method is used to reduce the non-linear partial differential equations to ordinary non-linear differential equations. The influences of gradient con- stants and control voltage on the nonlinear vibration are discussed. The results show that the positive voltage decreases the amplitude while the negative voltage increases the amplitude of the plate. With the increase of N, the oscillation amplitude increases.

关 键 词：功能梯度材料 压电 悬臂板 一阶剪切变形理论 

分 类 号：O322[理学—一般力学与力学基础]