Buckling and nonlinear dynamics of elastically coupled double-beam systems

• Damped transverse vibrations of elastically coupled double-beam systems.
• Analysis of steady-states and buckling bifurcations.
• Mode jumping and symmetric breaking (secondary) bifurcations.
• Existence and structure of the global regular attractor.
• Analysis of the basins of attraction when the system uncouples.

This paper deals with damped transverse vibrations of elastically coupled double-beam system under even compressive axial loading. Each beam is assumed to be elastic, extensible and supported at the ends. The related stationary problem is proved to admit both unimodal (only one eigenfunction is involved) and bimodal (two eigenfunctions are involved) buckled solutions, and their number depends on structural parameters and applied axial loads. The occurrence of a so complex structure of the steady states motivates a global analysis of the longtime dynamics. In this regard, we are able to prove the existence of a global regular attractor of solutions. When a finite set of stationary solutions occurs, it consists of the unstable manifolds connecting them.