摘要
对作大范围运动功能梯度材料矩形薄板的刚柔耦合动力学问题进行了研究.以连续介质力学为基础,在柔性薄板面内变形中考虑了传统建模方法忽略的二次耦合变形量,采用假设模态法对薄板变形位移进行离散,运用拉格朗日方程推导了大范围运动功能梯度材料板的刚柔耦合动力学方程.对旋转运动下取不同功能梯度指数的悬臂功能梯度板的动力学行为进行仿真,比较了本文建立的一次近似耦合模型和传统不计耦合变形项的零次近似模型.结果表明,随着转速的提高,传统零次模型发散,而本文模型收敛,能够较好地描述系统动力学行为.利用本文建立的一次近似模型,研究了功能梯度指数对转动功能梯度板变形的影响,研究表明,随着功能梯度指数的增大,板的横向变形也增大.通过求解旋转FGM板在恒定转速下的固有频率,进一步分析了功能梯度板材料组分变化对板振动特性的影响.
The rigid-flexible coupling dynamics of a rectangular functionally graded thin plate undergoing large o- verall motion is investigated. Based on continuum medium mechanics, The governing equations of motion are estab- lished using assumed mode method and Lagrange's equations, for the rectangular functionally graded thin plates un- dergoing large overall motions. The second order coupling deformation variable, which is ignored in traditional method, is considered in this paper. The dynamics of cantilever plates with different functionally graded coefficiernt undergoing rotation are simulated and the deformation results of first order approximation model are compared with those of traditional zero order appoximation model. It is shown that, as the rotating velocity increase,the traditional model divergences while the first order model converges. The first order model describes the dynamic behavior of the system better. The effects of the functionally graded index on the deformation of plates are studied. Studies have shown that, with the increases of the functionally graded index, the greater the lateral deformationthe of plate. By solving the natural frequencies of rotating FGM plate under a constant speed,the impact of of changes in the materi- al composition of FGM plates on the plate vibration characteristics is further studied.
出处
《动力学与控制学报》
2013年第4期329-335,共7页
Journal of Dynamics and Control
基金
国家自然科学基金资助项目(11272155
11132007
10772085)
江苏省"333工程"(BRA2011172)
中央高校基本科研业务费专项资金资助(30920130112009)~~
关键词
大范围运动
功能梯度材料板
功能梯度指数
动力刚化
固有频率
large overall motions, functionally graded plates, functionally graded index, dynamic stiffe-ning, natural frequencies