Nonlinear parametric vibration of spinning pipes conveying fluid with varying spinning speed and flow velocity

Abstract

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.