基于初应力法的作大范围运动柔性梁动力学建模理论研究

研究了初应力法的作大范围运动柔性梁的建模理论.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梁进行离散,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梁刚-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梁的结构动力学方程进行数值仿真,对零次近似模型、一次近似模型、初应力法动力学模型的仿真结果进行分析,揭示三种模型的动力学性质的差异.

Study on Dynamic Modeling of Flexible Beams Undergoing Large Overall Motion Based on Initial Stresses Method

The coupling dynamic modeling of flexible beams was studied by using initial stresses method.Based on continuum medium mechanics,the rigid-flexible coupling dynamic model for flexible beams,with free large overall motions,was established.The finite element method was used for system discretization and coupling dynamic equations of flexible beams with a rotating rigid body were obtained by use of Jourdain's velocity variational principle.The dynamic properties of a rotating beam in the non-inertial referene frame were studied quantitatively.In the cases of different rotating speeds for the beam,the numerical results of zero order approximate dynamic model was compared with those of one order approximate model and initial stresses model.The difference of the dynamic property among these models wss revealed.