Stability analysis in some strongly prestressed rectangular plates

We consider an evolution plate equation aiming to model the motion of the deck of a periodically forced strongly prestressed suspension bridge. Using the prestress assumption, we show the appearance of multiple time-periodic uni-modal longitudinal solutions and we discuss their stability. Then, we investigate how these solutions exchange energy with a torsional mode. Although the problem is forced, we find a portrait where stability and instability regions alternate. The techniques used rely on ODE analysis of stability and are complemented with numerical simulations.