作大范围运动矩形板的动力学建模理论研究

研究了初应力法的作大范围运动矩形板的建模理论。根据连续介质理论,考虑应变-位移中的非线性项,用一致质量有限元法对柔性板进行离散,基于Jourdain速度变分原理导出定轴转动下大范围运动为自由的柔性板刚-柔耦合动力学方程。从其刚柔耦合动力学方程出发,考虑在大范围运动已知情况下的结构动力学方程。通过引入准静态概念,把其结构动力学方程转化为准静态方程。对纵向和横向变形节点坐标进行坐标分离,解出与纵向变形相关的准静态方程,得到准静态时的纵向应力表达式,从而获得附加刚度项;并对此非惯性系下作大范围运动柔性板的结构动力学方程进行数值仿真,验证了采用初应力法柔性板的动力学建模方法来计算经历大范围运动的不规则柔性板的动力学响应是可行的,体现了初应力法对柔性板建模的优越性。

Study on dynamic modeling of rectangular plates undergoing large overall motion

In this paper,the coupling dynamic modeling of rectangular plates is studied by using initial stresses mothed.Based on continuum medium mechanics,the rigid-flexible coupling dynamic model for flexible plate,with large overall motions being free,is established.The finite element method is used for system discretization and coupling dynamic equations of flexible plate with a rotating rigid body are obtained by use of Jourdain's velocity variational principle.Dynamic properties of a rotating plate in the non-inertial reference frame are studies quantitatively.In cases of different rotating speeds for the plate,the numerical results of conventional model are compared with those of initial stresses model.The difference of the dynamic property between initial stresses model and conventional model is revealed.At the same time,numerical difference between the plate modeling and beam modeling is also compared.The superiority and reliability of irregular plate undergoing large overall motion is validated in this paper.