Abstract The mathematical model and non-smooth dynamics of a two-segment articulated pipe conveying fluid with the upper segment subjected to a one-sided rigid stop is investigated. To determine the effect of the one-sided rigid stop on the impacting behaviors of the articulated pipe under various geometrical and physical parameters, the nonlinear equations of motion combined with the rigid impacting condition are established and solved by a fourth-order Runge-Kutta algorithm. In the linear analysis, the stabilities and critical flow velocities of the articulated pipe are analyzed by examining the linearized equations without the rigid stop. Typical results of stability boundaries are compared to those reported previously and good agreement is obtained. In the nonlinear analysis, bifurcation diagrams and phase portraits of the responses of the upper and lower segments are presented and discussed by considering the effects of mass ratio, stiffness ratio, stop gap and coefficient of restitution. Periodic and chaotic vibro-impact oscillations are observed, with a particular interest in the detecting of the possibility of stick-slip motions which show the non-smooth vibrating characteristics of this rigid impacting system. It is shown that the coefficient of restitution for impact has a great effect on the chaotic oscillations and stick-slip motions of the pipe. Results obtained in this work highlight the complexity of the nonlinear impacting dynamics of articulated pipes conveying fluid with a rigid stop. It is also expected, in the near future, to extend the basic idea of this work to explore the nonlinear responses of flexible pipes and hoses conveying fluid subjected rigid stops by introducing a multi-segment articulated pipe model.

中文翻译：

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单侧刚性止动作用下铰接管输送流体的非光滑动力学

摘要 研究了上段受单向刚性挡块的两段铰接管输送流体的数学模型和非光滑动力学。为了确定在各种几何和物理参数下单侧刚性挡块对铰接管冲击行为的影响，结合刚性冲击条件建立非线性运动方程并通过四阶Runge-Kutta算法求解. 在线性分析中，通过检查没有刚性挡块的线性化方程来分析铰接管的稳定性和临界流速。将稳定性边界的典型结果与先前报道的结果进行比较，并获得了良好的一致性。在非线性分析中，通过考虑质量比、刚度比、止动间隙和恢复系数的影响，提出并讨论了上下段响应的分叉图和相图。观察到周期性和无序的振动冲击振荡，特别感兴趣的是检测粘滑运动的可能性，粘滑运动显示了这种刚性冲击系统的非平滑振动特性。结果表明，冲击恢复系数对管道的混沌振荡和粘滑运动有很大的影响。在这项工作中获得的结果突出了带有刚性挡块的铰接管输送流体的非线性冲击动力学的复杂性。还预计，在不久的将来，