端部约束悬臂输流管道的非线性动力学特性

Nonlinear dynamic characteristics of end restraint cantilever fluid-conveying pipe

针对悬臂端受线性弹簧支承和扭转弹簧约束的约束悬臂输流管道,采用分岔图、相平面图、Poincare截面和Lyapunov指数等非线性振动的数值仿真方法,研究其在自激参数激励外激励联合激励作用下的非线性动力学特性,分析系统出现周期和混沌运动响应的参数条件,揭示其通向混沌的途径,探寻各参数对输流管道振动特性的影响规律和各参数之间的相互制约关系.数值仿真结果表明,管道系统随质量比、端部约束刚度和管道粘弹性系数的不同,分别呈现周期、概周期、阵发性和混沌运动多种响应形式,系统通过倍周期分岔或阵发性进入混沌,通过倍周期倒分岔脱离混沌.

For the restraint cantilever fluid-conveying pipe supported by linear spring and restrained by torsion spring,the nonlinear dynamic characteristics under the combined self-excitation,parameter-excitation and external excitation were investigated by means of such nonlinear numerical simulation methods as bifurcation diagram,phase plane,Poincare section and Lyapunov exponent. The parameters conditions for the system to exhibit the periodic and chaotic motion response were analyzed. The path towords chaos was revealed. The effect regularity of various system parameters on the vibration characteristics of the pipe and the restricting relationship among the parameters were discussed. The numerical simulation results show that the pipe system exhibits the multiple response forms such as the periodic motion,quasi-periodic motion, intermittent chaos and chaotic motion at different mass ratio,end restraint stiffness and visco-elastic coefficient of pipe. The system gets into the chaotic motion by the period-doubling bifurcation and intermittent chaos,and deviates the chaotic motion by the inverse period-doubling bifurcation.