Analysis of dynamic instabilities in bridges under wind action through a simple friction-based mechanical model

In the field of stability of structures under nonconservative loads, the concept of follower force has long been debated by scientists due to the lack of actual experimental evidence. Bigoni and Noselli's work [2] aimed to investigate flutter and divergence instability phenomena through a purely mechanical model with Coulomb friction represents a praiseworthy attempt to shed light on this issue. A two-degree-of-freedom (DOF) system, conceived as a variant of the Ziegler column, was set up experimentally. The follower load was induced by a frictional force acting on a wheel mounted at the column end, so that the rolling friction vanishes and the sliding frictional force keeps always coaxial to the column, thus representing a tangential follower force. Along this research line, in this contribution a model is elaborated that stems from the analysis of an elastically supported rigid plate that represents the behaviour of a bridge deck suspended on springs and subjected to a wind-induced force. The wind force has been simulated by a Coulomb friction force acting on a wheel mounted on the plate aerodynamic centre, so that the sliding friction force keeps perpendicular to the plate axis throughout the system motion, thus representing a follower force. To properly reproduce the wind force, the friction force is applied to the wheel by a lever mechanism wherein one of the two lever arms involves the plate rotation via a particular circular guide. The corresponding equations of motion of the bridge deck are derived in a completely dimensionless form. Depending on the mechanical characteristics of the plate and the magnitude of the friction force, stability, flutter or divergence phenomena may occur. The occurrence of these phenomena is numerically investigated by integration of the equations of motion. The development of an experimental framework of the model to corroborate these intuitions is the object of an ongoing research.