Parametric vibration of a nonlinearly supported pipe conveying pulsating fluid

Changes of fluid speed may cause large vibrations in the pipe system. Generally, the fluid speed in a pipe system may not be constant all the time but has an oscillating property of the fluid, such as pulsating fluid. When a pipe conveys pulsating fluid, its dynamic response is significantly affected by the fluid. This paper investigates the vibration characteristics of a pipe conveying pulsating fluid with nonlinear supports at both ends. Based on the Hamilton principle, the governing equations and the boundary conditions for the pipes conveying pulsating fluid are determined. The multi-scale method combined with the modal revision method is introduced to obtain the approximate analytical results of the system steady-state response. Subsequently, the approximate analytical solution is verified numerically by the differential quadrature element method. The effects of the linear support stiffness, the nonlinear support stiffness, the fluid speed, and the viscoelastic coefficient on the stability boundary of parametric resonance are investigated. The effects of system parameters on steady-state responses of the pipe are also discussed in detail. The results reveal that the two methods are in good agreement. And it is shown that the linear support stiffness affects not only the parametric resonance amplitude but also the resonance region, while the nonlinear support stiffness only affects the parametric resonance amplitude, but not the resonance region.