Fluttering and dancing elastic rods: the dynamics of the elastica subject to follower and configurational forces*

Using the elastica theory, configurational or 'Eshelby-like' forces will be shown to arise in elastic structures when a change in configuration is possible, with a related release of energy. Configurational forces will be shown to influence the dynamics of a falling body connected through an elastic rod to a sliding sleeve, so that a damped nonlinear oscillator results, which generates a complex motion, nicknamed 'dancing'.
Finally, The dynamics of an elastic rod in a cantilever configuration and subject to a tangential follower load of the ‘Ziegler type’ at its end (the ‘Pfluger problem’) is addressed. This structure is subject to a Hopf bifurcation, corresponding to the initiation of the ‘flutter instability’. A new experimental set-up is presented as designed, produced and tested to realize the follower load. Experiments provide the evidence of flutter and divergence instability and result in the first proof that damping sources have a destabilizing effect on the system (the so-called ‘Ziegler paradox’).