Global and exponential attractors for a suspension bridge model with nonlinear damping

Abstract

In this manuscript, for the first time in the literature, we study the asymptotic analysis of compact global attractors of oscillations in suspension bridges, modeled by the Timoshenko Theory. Instead of showing the existence of an absorbing set, we prove the system is gradient and asymptotically smooth and hence obtain the existence of a global attractor, characterized as an unstable manifold of the set of stationary solutions. We use the recent quasi-stability theory developed by Chueshov and Lasiecka [4], [5] directly on a bounded positively invariant set to prove the smoothness and finite fractal dimension of the attractor, as well as the existence of exponential attractors and determining functionals.