Stochastic vibration analysis of damaged stay cable structures

<p indent="0mm">Cable structures are susceptible to damage due to material aging, overloading, and other factors. Besides, the high flexibility of cables may also lead to large vibration amplitudes, exacerbating damage and potentially compromising the safety of entire bridges. Thus, accurately predicting the dynamic response of damaged cable structures and analyzing their vibration characteristics are crucial for effective health monitoring and appropriate repair treatments. However, the current studies are mainly focused on the deterministic vibration analysis of damaged cables, overlooking the stochastic nature of real excitations, or are limited to the random vibrations of undamaged cables. Consequently, it is urgent to study the random vibration of damaged cables. This study employs a Gaussian white noise model to represent the real stochastic dynamic loads and researches the nonlinear stochastic vibration response of damaged stay cable structures. First of all, the nonlinear stochastic dynamic model for the coupled in-plane and out-of-plane motions of the damaged cable system is formulated, encompassing the determination of the static configuration of the damaged stay cable, the derivation of the motion differential equations, and discretization by using the Galerkin’s method. Subsequently, the Fokker-Planck-Kolmogorov (FPK) equation is solved using the radial basis function neural network (RBFNN) method to derive the probability density function and mean value of the system′s steady-state response under varying parameters. The results indicate that increasing damage severity and range significantly amplifies the displacement response, while the effect of damage location is negligible. Additionally, the MVs of in-plane displacement demonstrate a linear trend with changes in damage severity and range. Monte Carlo simulations validate the accuracy and applicability of the numerical methods employed. These findings provide new theoretical insights for assessing the operational status of stay cable systems and facilitating effective health monitoring.