作大范围运动弹性梁的非线性稳定性分析

摘要

The dynamical equatons of a flexible beam in large overall motions considering the coupling deformaton of its middle lines is established and the difference between the coupling model and the clssical model is presented.Using the ‘Energy-Momentum’mcthod,nonlinear stability of the equilibrum in each case is analyzed.The results show that the system will lose stability when the rotating angular velocity is greater than its fundamental frequency in classical dynamical model.However,the system can keep stable in any rotating angular velocity in the coupling dynamical model.%本文建立了作大范围转动弹性梁考虑了中线变形之间相互耦合的动力学控制方程。比较了传统动力学模型与本文所建立的耦合动力学模型之间的差异，用能量-动量矩方法，对两种模型进行了稳定性分析。分析结果表明，在传统力学模型中，当转动角速度小于弹性梁的基频时，系统稳定；反之，系统将失稳。而耦合动力学模型在转动角速度为高速时，系统都是稳定的，这与实际情形相符。