Identification of horseshoes chaos in a cable-stayed bridge subjected to randomly moving loads

• Cable-stayed bridge loaded by a train of moving forces with stochastic velocity.
• Modelling of the dynamics of cable-stayed Bridge by a single nonlinear-dimensional equation.
• The moving loads have been modelled as equal weights moving with random velocity.
• Stochastic velocity and cables number have an effect on the inhibition of horseshoes chaos.
• The deviation of stochastic velocity can enlarge the possible chaotic domain of the system.

In this paper, the dynamic response of cable-stayed bridge loaded by a train of moving forces with stochastic velocity is investigated. The cable-stayed bridge is modelled by Rayleigh beam with linear elastic supports. The stochastic Melnikov method is derived and the mean-square criterion is used to determine the effects of stochastic velocity and cables number on the threshold condition for the inhibition of smale horseshoes chaos in the system. The results indicate that the intensity of the random component of the loads velocity can be contributed to the enlargement of the possible chaotic domain of the system, and/or increases the chances to have a regular behavior of the system. On the other hand, the presence of cables in cable-stayed bridges system increases it degree of safety and paradoxically can be contributed to its destabilization. Numerical simulations of the governing equations are carried out to confirm the analytical prediction. The effect of loads number on the system response is also investigated.