Stochastic unilateral free vibration of an in-plane cable network

• Stochastic unilateral vibration of a cable-cross-tie system is examined.
• Stochastic disturbance is used to account for uncertainty in wind-induced vibration.
• Stochastic Approximation (SA) is employed to estimate amplitude-dependent dynamics.
• Monte Carlo sampling methods are used to verify the SA results.
• Numerical studies confirm effects of nonlinear behavior and stochastic vibration.

Cross-ties are often used on cable-stayed bridges for mitigating wind-induced stay vibration since they can be easily installed on existing systems. The system obtained by connecting two (or more) stays with a transverse restrainer is designated as an “in-plane cable-network”. Failures in the restrainers of an existing network have been observed. In a previous study [1] a model was proposed to explain the failures in the cross-ties as being related to a loss in the initial pre-tensioning force imparted to the connector. This effect leads to the “unilateral” free vibration of the network. Deterministic free vibrations of a three-cable network were investigated by using the “equivalent linearization method”.Since the value of the initial vibration amplitude is often not well known due to the complex aeroelastic vibration regimes, which can be experienced by the stays, the stochastic nature of the problem must be considered. This issue is investigated in the present paper. Free-vibration dynamics of the cable network, driven by an initial stochastic disturbance associated with uncertain vibration amplitudes, is examined. The corresponding random eigen-value problem for the vibration frequencies is solved through an implementation of Stochastic Approximation, (SA) based on the Robbins–Monro Theorem. Monte-Carlo methods are also used for validating the SA results.