Generalized power-law stiffness model for nonlinear dynamics of in-plane cable networks

Cross-ties are used for mitigating stay-cable vibration, induced by wind and wind-rain on cable-stayed bridges. In-plane cable networks are obtained by connecting the stays by transverse cross-ties. While taut-cable theory has been traditionally employed for simulating the dynamics of cable networks, the use of a nonlinear restoring-force discrete element in each cross-tie has been recently proposed to more realistically replicate the network vibration when snapping or slackening of the restrainer may be anticipated. The solution to the free-vibration dynamics can be determined by "equivalent linearization method". In an exploratory study by the authors a cubic-stiffness spring element, in parallel with a linear one, was used to analyze the restoring-force effect in a cross-tie on the nonlinear dynamics of two simplified systems. This preliminary investigation is generalized in this paper by considering a power-law stiffness model with a generic integer exponent and applied to a prototype network installed on an existing bridge. The study is restricted to the fundamental mode and some of the higher ones. A time-domain lumped-mass algorithm is used for validating the equivalent linearization method. For the prototype network with quadratic-stiffness spring and a positive stiffness coefficient, a stiffening effect is observed, with a ten percent increment in the equivalent frequency for the fundamental mode. Results also show dependency on vibration amplitude. For higher modes the equivalent nonlinear effects can be responsible for an alteration of the linear mode shapes and a transition from a "localized mode" to a "global mode".