Response Analyses of Tuned Mass Dampers to Structures Exposed to Vortex Loading of Simiu-Scanlan Type

Vortex-induced loads on slender one-dimensional structures vibrating at lock-in conditions consist of a self-induced part in phase with the velocity of the structure in addition to an additive, almost harmonially varying component representing the same type of load as the vortex-induced force on a fixed cylinder. Simiu and Scanlan (1996 Wind Effects on Structures. New York: John Wiley & Sons Inc.) have proposed a widely used model for the self-induced part of the load based on a van der Pol oscillator. The aim of this paper is to investigate the optimal design of tuned mass dampers for such a load model. The method of analysis is based on the averaging method (Krylov-Bogoliubov-Mitropolsky first order perturbation analysis) for weakly non-linear systems. Several interesting findings have come out of the analysis. First, it is shown that, if the additive loading is omitted, the vibrations will be completely removed in an interval of the frequency tuning in contrast to the case of harmonic loading, where total damping of the primary system at optimal tuning is only possible when no structural damping is present. The stability of the theoretically possible motions is checked at di!erent levels of viscous damping in the tuned mass damper. From this analysis it is concluded that introducing less damping than used for harmonic load, in order to achieve optimal results, may prove more efficient as far as van der Pol oscillator load model is concerned. The theory has been applied to passive damping control of the Rio-Niterói steel girder bridge, Rio de Janeiro, which is occasionally severely exposed to vortex-induced vibrations.