In this paper, a nonlinear parameter-excited model of spinning pipes conveying fluid is proposed by considering the spinning speed and flow velocity are perturbed periodically, and the stability and nonlinear parametric vibrations of such system are studied analytically and numerically. With taking the viscoelastic material and geometrical nonlinearity due to extensible pipe axis into account, the differential equations governing two transverse vibrations of the pipe are derived by the Hamilton principle. The system stability is then analyzed via the multiple scales method, and the nonlinear responses and spatial vibration shapes are investigated using numerical simulation. The contributions of some significant parameters on the vibrations of the system are discussed in detail. It is revealed that not any other motion but combination parametric resonance with quasi-periodic motion mode can occur in the present system, and it is induced fully by the periodically perturbed fluid. A perturbed spinning motion cannot result in any parametric resonance, however it has an opposite effect on the parametric vibrations as compared to that with constant spinning speed. The flow velocity, nonlinearity and viscoelastic damping all have significant impacts on the present parametric vibrations. Moreover, the pipe performs different aperiodic whirling motions in the first two modes, and the perturbed spinning speed will lead to a gentler motion of the pipe as compared to the case of constant spinning speed.

本文通过考虑旋转速度和流速的周期性扰动，提出了一种输液旋转管的非线性参数激励模型，并对该系统的稳定性和非线性参数振动进行了分析和数值研究。考虑到粘弹性材料和由于可延伸的管轴引起的几何非线性，通过汉密尔顿原理推导了控制管的两个横向振动的微分方程。然后通过多尺度方法分析系统稳定性，并使用数值模拟研究非线性响应和空间振动形状。详细讨论了一些重要参数对系统振动的贡献。揭示了在本系统中不会发生任何其他运动，而是具有准周期运动模式的组合参数共振，并且它是由周期性扰动的流体完全诱发的。扰动的旋转运动不会导致任何参数共振，但是与恒定旋转速度相比，它对参数振动具有相反的影响。流速，非线性和粘弹性阻尼都对当前的参数振动产生重大影响。而且，在前两种模式下，管子执行不同的非周期性旋转运动，并且与恒定旋转速度的情况相比，扰动的旋转速度将导致管子的运动更缓和。扰动的旋转运动不会导致任何参数共振，但是与恒定旋转速度相比，它对参数振动具有相反的影响。流速，非线性和粘弹性阻尼都对当前的参数振动产生重大影响。而且，在前两种模式下，管子执行不同的非周期性旋转运动，并且与恒定旋转速度的情况相比，扰动的旋转速度将导致管子的运动更缓和。扰动的旋转运动不会导致任何参数共振，但是与恒定旋转速度相比，它对参数振动具有相反的影响。流速，非线性和粘弹性阻尼都对当前的参数振动产生重大影响。而且，在前两种模式下，管子执行不同的非周期性旋转运动，并且与恒定旋转速度的情况相比，扰动的旋转速度将导致管子的运动更缓和。