悬臂输流管道的运动分岔现象和混沌运动

研究受约束悬臂输流管道的稳定性和运动分岔问题.在静态与动态失稳区域边界上的一个交叉点附近,用理论分析的方法详细研究了该系统可能发生的复杂运动和运动分岔现象.在动态失稳区域内发现了输流管道的概周期运动和由于概周期运动环面破裂而导致混沌的现象.理论分析结果与数值模拟结果相吻合.

BIFURCATIONS AND CHAOTIC MOTIONA OF A CANTILEVERED PIPE CONVEYING FLUID

In this paper, we have studied some local stability and bifurcation problems of a cantilevered pipe conveying fluid with the motion limiting constraints and a linear spring support. The local behavior of the system in the neighborhood of a doubly degenerate point was analyzed by using some qualitative reduction methods in dynamical system theory, such as center manifold and Birkhoff's normal form theory. The analytical results obtained are found to be in good agree-ment with that obtained by means of numerical simulations in our early work. Furthermore, the analytical unfolding results show that the quasi-periodic motions may occur in certain parameter range in the system, which could not be detected in the early work using numerical method.In addition we found that as the parameter values of the velocity of flow and the stiffness of the spring support vary from the doubly degenerate point to the sub region of chaotic motions detected in the early work along some boundary line in the stability region of the system chaotic motions occur as the results of the breakup of the quasi-periodic torus surface. It is known to be a different route to chaos from that of "periodic-doubling bifurcation" route which has been detected in this system earlier.