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

Abstract

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.

Boundary stabilization for axially moving Kirchhoff string under fractional PI control

“…The boundary stabilization is also available for two kinds of nonlinear axially moving beam systems in [27,28]. In addition to vibration control, the dynamics or vibration behavior of the axially moving structures also becomes an important topic and we refer this to [29][30][31][32][33][34].…”

High‐gain stabilization for an axially moving beam under boundary feedback control

“…In Hassan and Tatar, 39 high‐gain adaptive regulators are designed to establish an exponential stability result for the Timoshenko beam equation subject to two control inputs at the right end by means of the multiplier method. In addition, for the investigation of the vibration control of some axial moving systems, we refer the interested reader to earlier research 40–42 …”

“…In addition, for the investigation of the vibration control of some axial moving systems, we refer the interested reader to earlier research. [40][41][42] Introduce nondimensional variables…”