一类刚-柔耦合系统的建模与稳定性研究

MODELLING AND STABILITY INVESTIGATION OF A RIGID FLEXIBLE COUPLING SYSTEM

对于由中心刚体带有柔性梁附件组成的这一类简单刚柔耦合系统，目前文献广泛采用的ＥｕｌｅｒＢｅｒｎｏｕｌｉ梁模型中考虑的刚柔运动耦合项有严重的缺陷．本文对于物理本构关系线性的有限变形梁，分别采用微元法和变分法建立了该系统大挠度非线性动力学方程组．本文使用严格的方法来研究此非线性耦合动力学模型，采用能量动量矩组合方法构成Ｌｉａｐｕｎｏｖ函数，严格证明了此非线性系统平凡解的积分范数稳定性以及具有鲜明物理意义的最大模范数稳定性．本文对文献中引用的三类线性化模型，采用假设模态法，对中心刚体匀速转动时梁的振动作了数值仿真，进一步验证了本文的结论．上述结果，对选择刚柔耦合系统正确的动力学模型是有益的．

For the simple Rigid Flexible Coupling system with a central rigid body and a mounted cantilever beam, the mathematical models of Euler Bernoulli beam in earlier papers have serious defect. In the present work, a nonlinear mathematical model of the system with a finite deforming beam on the assumption that its constitutive relation in linearly elastic, using the Differential Element Method and Variational Method, is obtained. In using strict method to analyse this nonlinearly coupling dynamic system, we use the Energy Momentum Method to prove the Integral Norm Stability of the trivial solution and the Maximum Value Norm Stability of the beam's displacement vector. Furthermore, for the three sorts of linearization model used in earlier papers, we make a numerical simulation of the beam's vibration when the rigid body is rotating steadily by using Assumed Mode Approach. This proved our theoretical conlusion. The results in this paper have the advantage of selecting exact dynamic model for Rigid Flexible Coupling System.