higher order moments of eigenvalue and eigenvector distributions for the nonlinear stochastic dynamics of cable networks

Abstract Cross-ties are employed on cable-stayed bridges to reduce wind-induced stay vibration. The occurrence of a number of failures has motivated investigations on the nonlinear dynamics of these systems. The non-linear behavior is possible at incipient failure of the cross-tie. This paper combines the features of the Equivalent Linearization Method, recently derived to study non-linear behavior in the cross-ties at moderate stay vibration amplitudes, with implementation of the Stochastic Approximation (SA) to account for the presence of parameter variability during aeroelastic vibration. The problem becomes an equivalent random eigenvalue problem with eigenvalues (equivalent frequencies) depending on a random vibration amplitude parameter. Novel implementations of the SA are considered to evaluate higher-order statistical moments of eigenvalue distributions; the consequent randomness in the eigenvectors is also examined