Stability analysis of a pipe conveying fluid with a nonlinear energy sink

This paper considers the global stability problem of the system comprising a pipe conveying fluid and a nonlinear energy sink (PCF-NES) system. First, a quadratic form model containing a gradient term of a convex function is obtained from a high-order partial-differential-equation model of the PCF-NES system using the Galerkin approximation approach. Energy and disturbance functionals are then established based on this model. Second, a Lyapunov function is constructed based on the first-order characteristic of the convexity and energy disturbance technique to prove the global exponential stability of the approximated PCF-NES system. Finally, theoretical results are verified using numerical simulations and the positive effect of the NES on the vibration control of the entire PCF is discussed.