大范围运动矩形板动力刚化分析

针对大范围运动下弹性矩形板，采用有限元技术和Lagrange方程建立了系统刚柔耦合一次近似动力学方程组．不同于传统动力学建模方法，本文采用两个弧长变量和一个笛卡尔坐标变量来描述板的变形，利用有限元方法离散，在动力学方程中得到了动力刚度项．数值仿真表明，在大范围运动下，传统的动力学模型不能正确的预示系统动力学行为；而本文动力学模型能够较好的预测系统的动力学行为，且比采用假设模态离散板变形的方法更为精确．

Dynamic analysis of rectangular plate undergoing overall motion

The rectangular plate undergoing overall motions was investigated. The dynamic equations were derived through the Finite Element Method and Lagrange equations. Different from the conventional linear modeling method which employs three Cartesian deformation variables, the present modeling method used two non-Cartesian variables along with one Cartesian variable to describe the elastic deformation. Therefore the dynamic stiffness terms was captured. The numerical study demonstrated that the equations of motion presented here are more reliable and accurate than the traditional dynamic equations. Some errors will appear if the assumption modal method is used to describe the deformation of flexible plate undergoing overall motions.