prof. Piotr Przybyłowicz, SIMR, PW. Destabilization in a non-conservative system brought about by dry friction – discussion on the Trento Experiment

The history of studies on stability of columns subjected to compressive forces goes back to Leonhard Euler who analyzed static buckling of elastic compressed rods and formulated theory of buckling now being used in the academic courses of strength of materials. The problem was refreshed and attracted much attention of scientists in structural mechanics in the 60s. of the last century when flutter was theoretically found as a result of so called follower forces that change their direction, following the current configuration of a system they act on. A bit earlier, Hans Ziegler found flutter instability in a discrete two-degree-of-freedom double-rod system, now just well known as the Ziegler column. An impressive overview of rich literature on systems under follower forces was given by Isaac Elishakoff who wrote Essay on the So-Called Follower Forces, being inspired by discussion between Warner Koiter and Yoshihiko Sugiyama on the existence and physical meaning of such systems. In the recent years, Italian researchers from University of Trento: Davide Bigoni, Giovani Noselli and Daniele Zaccaria carried out an experiment which, according to the authors, was an evidence for flutter in the Ziegler system. In the paper, a detailed analysis of stability of the Trento experiment is presented and the results are compared with those known for the original formulation of the problem. Special attention is paid to the existence of flutter and divergence in the tested system in order to answer the basic question of whether and to what extent the experiment reflects dynamical properties of the ideal Ziegler column.