Stochastic modelling and stability of suspension bridge

In this paper we consider the problem of stability of suspension bridges in the presence of random wind forces acting on the deck and the suspension cables. Total mechanical energy given by the sum of all kinetic and elastic potential energies of the structure, is used as a Lyapunov functional. Assuming negligible mechanical friction and viscous damping, it is seen that the system is conservative and that random wind forces can destabilize the system. In the presence of structural damping, provided by piezo ceramic layers or other smart materials, it is seen that the system is asymptotically stable. This is clearly illustrated by numerical results presented in the final section of the paper.