Review Study on Nonlinear Modeling Issues Associated with the Dynamics of In-Plane Cable Networks

This study summarizes a decade-long research activity, devoted to the examination of the nonlinear dynamics of in-plane cable networks on cable-stayed bridges. Nonlinearity is triggered by amplitude-dependent, internal restoring force behavior of the cross-ties, connecting two adjacent stays. The work originates from an earlier study by the first author. The study reviews the main contributions that include the derivation of the Equivalent Linearization Method to solve the amplitude-dependent eigenvalue-eigenvector problem of the network, and the use of Stochastic Approximation to examine stochastic dynamics, induced by random amplitudes at the onset of aeroelastic vibrations. A random amplitude parameter is used to characterize the nonlinear behavior in the restrainer, and to simulate imperfections, malfunctioning and modeling simplifications. A three-stay, one-restrainer network, installed on the Fred Hartman Bridge (Houston, Texas, USA) is employed to illustrate the main results.