Design of tuned mass dampers incorporating wire rope springs: Part I: Dynamic representation of wire rope springs

Two mathematical models for describing the effective stiffness and the equivalent viscous damping ratio of wire rope springs, as amplitude dependent, were developed. Twenty-four springs were tested in free vibration and the displacement decays were recorded. The free vibration time history was used to calculate the effective stiffness and the equivalent viscous damping ratio. For each displacement amplitude, the effective stiffness was determined from the observed period of vibration. The equivalent viscous damping ratio was determined from the logarithmic decrement of the velocity between the points of zero potential energy. The proposed models are semi-empirical in nature and require no testing since all parameters are fully determined from the physical properties of springs.