计及热应变的空间曲梁的刚-柔耦合动力学

研究带中心刚体的作大范围运动的空间曲梁的刚-柔耦合动力学.结合混合坐标法和绝对坐标法的特点,取与中心刚体大范围运动有关的变量和柔性梁各单元节点相对中心刚体连体基的位移和斜率作为广义坐标,建立了一种新的柔性梁的刚柔耦合模型.基于精确的应变和位移的关系式,根据Jourdian速度变分原理,建立了带中心刚体柔性曲梁的有限元离散的动力学方程.数值对比了空间曲梁系统和空间直梁系统的刚柔耦合动力学性质,用能量守恒规律验证了文中曲梁模型的合理性.在此基础上,在应变能中计及热应变,研究温度增高引起的曲梁的热膨胀对系统的动力学性态的影响.

RIGID-FLEXIBLE COUPLING DYNAMICS OF A CURVIC BEAM CONSIDERING THERMAL STRAIN

In this paper,rigid-flexible coupling dynamics of a curvic beam attached with a central rigid body undergoing spatial large overall motion,is investigated.Combining the characteristics of the hybrid coordinate formulation and the absolute nodal coordinate formulation,we take the relative nodal displacement and slope of each beam element with respect to the body-fixed frame of the hub,and the variables related to the hub spatial motion,as the generalized coordinate system.A new method for rigidflexible dynamics is proposed.Based on precise strain-displacement relation,the rigid-flexible coupling equations of a dynamics system composed of a curvic beam and a central rigid body are derived using Jourdain velocity variational principle.Finite element method is employed for discretization.Simulation of the dynamic system is used to compare the dynamic characteristics of a straight beam system and a curvic beam system.The correctness of the proposed formulation is verified by energy conservation law.Furthermore,effect of thermal expansion,caused by temperature increase,on the dynamic performance of the system is investigated by including thermal strain into the strain energy.