Damping effects of nonlinear dampers on a shallow cable

Abstract

This study investigates the damping performance of nonlinear dampers on a shallow cable for vibration control. For this purpose, a method is presented to appreciate the system damping based on periodically forced vibration analysis. Furthermore, the reduced-order model for cable-damper systems in the literature is improved to analyze the near-resonant responses of the system and to consider two dampers installed respectively near the two cable ends. The method is then verified based on a cable attached with linear dampers and further applied to a shallow cable with one and two nonlinear viscous dampers. By grouping the damper and cable parameters appropriately, the damping curves of linear cable-damper systems are extended to shallow cables with nonlinear dampers, which are useful for damper design in practice. Extensive numerical studies are subsequently conducted for shallow cables of varying sag-extensibility parameter attached respectively with one viscous damper and two viscous dampers of different nonlinearity near cable ends, focusing on the sag affected vibration modes. The numerical results suggest that when the sag-extensibility parameter is small, a nonlinear damper is superior to a linear damper in terms of maximal damping effect for these modes, owing to the nonlinearity induced energy bleeding effect. Interestingly, in a particular range of the sag-extensibility parameter, the maximal damping of these modes achieved by a nonlinear damper is smaller than that by an optimal linear damper. It is also suggested that when two dampers are installed symmetrically near the cable ends, the damping effect for a symmetric mode is considerably different from the summation of the optimal damping achieved by each damper alone, and the optimal damper coefficient varies as well. The difference depends on the sag-extensibility parameter and the damper nonlinearity.