Limit Cycles in Vortex-Induced Vibrations: a Critical Analysis

摘要

The fluid-structure interaction in vortex-induced vibrations of circular structures is modelled as a non-linear damping force. The Van der Pol and Rayleigh oscillators are classic examples of physical systems, which attain a limit cycle under self-induced vibrations. Their application for the case of vortex-induced vibrations has a theoretical justification in Marris, who found an analogy with the Magnus effect for a rotating cylinder, because the lift force on a vibrating cylinder is produced by the non-symmetric boundary layer separation from the top and bottom surfaces. In accordance with the Rayleigh formulation, Vickery&Basu propose for the aerodynamic damping a parabolic relationship function of the rms oscillation. This approach is recommended in many international codes (e.g. Eurocode) for the design of circular structures with regard to cross-wind vibrations, even though the predictions result extremely conservative. Recent wind tunnel experiments performed at WISt (Ruhr-Universitat Bochum, Germany) on a circular cylinder in forced-oscillations evidenced a behaviour of the aerodynamic damping with positive curvature, which is in contrast with the negative curvature in Rayleigh oscillator. These experimental results require a critical analysis of the Vickery formulation and its theoretical background.