柔性体的刚-柔耦合动力学分析

RIGID-FLEXIBLE COUPLING DYNAMIC ANALYSIS OF FLEXIBLE BODY

对柔性梁的刚 柔耦合动力学特性进行分析 .从连续介质力学理论出发 ,在纵向变形位移中计及了耦合变形量 ,用Jourdain速度变分原理导出了柔性梁的刚 柔耦合动力学方程 .定量地研究了非惯性系下柔性梁的动力学性质 ,比较了在不同转速下零次近似模型和耦合模型的振动频率的差异 .为了确定零次近似模型的适用范围 ,引入与转速和基点加速度有关的相关系数 ,提出了零次近似模型的适用判据为相关系数小于 0 .1.在此基础上 ,进一步研究在大范围运动是自由的情况下柔性梁的大范围运动和变形运动的耦合机理 ,计算了带平动刚体的柔性梁的大范围运动规律 ,揭示零次近似模型和耦合模型的刚 -柔耦合动力学性质的根本差异 .

The rigid flexible coupling dynamic properties of a flexible beam are studied. Based on the continuum medium mechanics, the coupling term of deformation is included in the expression of longitudinal deformation. Coupling dynamic equations of the flexible beam are obtained from Jourdains velocity variational principle. The dynamic properties of a flexible and rotating beam in a non inertial reference frame are studied quantitatively for the first time. For different rotating speeds, the vibration frequency of the zero order approximate model is compared with that of the coupling model. The zero order approximate dynamic model usually has enough accuracy and computing efficiency for low rotating speed. A full new concept, the coupling coefficient, which is related to the rotating speed and the base acceleration, is put forward to determine the suitable range of the zero order approximate dynamic model. It is shown that the zero order approximate dynamic model is applicable only when the coupling coefficient is less than 0.1. Furthermore, the coupling dynamic properties of a flexible beam with free large overall motions is studied. The different dynamic properties between the zero order model and the coupling model are demonstrated by calculating the time history of large overall motions of a cantilever beam attached to a translational rigid body.