刚柔耦合系统的几何非线性运动稳定性

Stability of nonlinear motion of a rigid-flexible coupled system

针对由中心刚体与柔性附件所组成的平面型刚柔耦合系统,不仅研究柔性附件的横向弯曲变形对系统动态特性的影响,同时考虑柔性附件的拉伸变形、截面转角变化与弯曲变形的相互耦合作用,并且以非线性几何关系作为基本出发点,建立了柔性变形、姿态运动之间的非线性耦合动力学模型。基于上述非线性模型,利用能量积分构造Lyapunov函数,分别以中心刚体不转动和中心刚体匀速转动为无扰运动,证明了非线性系统关于姿态角速度、挠性变形位移和应变等扰动变量的稳定性。

The dynamics of a planar rigid-flexible coupled system were analyzed for a system consisting of a central rigid body and a flexible appendage. Most previous studies have only analyzed the effects of the transverse bending of a flexible beam on the system dynamics, but this paper also considers the axial deformation, the transverse bending deformation and the cross-section rotation. Nonlinear geometric relations were used to develop a nonlinear model of the rigid-flexible coupled system to relate flexible deformation and attitude motion. A selected Lyapunov function based on the energy function verifies the dynamic stability of the nonlinear system with attitude angular velocity, flexible deformation displacement and strain disturbances for two cases where the rigid body does not rotate and where the rigid body rotates at constant speed.