Flutter instability in structural mechanics: theory and experimental evidence

The present thesis summarizes the research activity in the field of elastic structures subject to tangential follower forces performed in the Instability Lab of the University of Trento. Elastic structures loaded by nonconservative positional forces are interesting from different perspectives. First, they are subject to flutter instability, a dynamical instability which remains undetected using static approaches. Second, in these structures dissipation plays a fundamental and destabilizing role. Third, a critical load calculated in the limit of vanishing dissipation is found to be smaller than the critical load calculated in the same structure where the dissipation is assumed absent 'from the beginning'. This behaviour is so peculiar that is usually referred to as 'the Ziegler paradox' and was never experimentally substantiated before. Flutter instability in elastic structures subject to follower load, the most important cases being the famous Beck's and Pflüger's columns (two elastic rods in a cantilever configuration, with an additional concentrated mass at the end of the rod in the latter case), have attracted, and still attract, a thorough research interest. In the present thesis, the effects of internal and external damping, crucial in the interpretation of experiments, have been investigated. Contrary to a common belief, it has been shown that the effect of external damping is qualitatively the same as the effect of internal damping, both yielding a pronounced destabilization paradox. This result corrects previous claims relative to destabilization by external damping of the Ziegler's and Pflüger's elastic structures. The major challenge in the research area of follower forces is the practical realization of these forces, which was previously obtained only for the case of the Ziegler double pendulum (a two-degrees-of-freedom elastic system subject to a tangential force). Therefore, an experimental setup to introduce follower tangential forces at the end of an elastic rod was designed, realized, validated, and tested, in which the follower action is produced by exploiting Coulomb friction on an element (a freely-rotating wheel) in sliding contact against a plate (realized by a conveyor belt). It is therefore shown that follower forces can be realized in practice and the first experimental evidence is given of the flutter and divergence instability of the Pflüger's column. Load thresholds for both the two instabilities are measured for the first time. Moreover, the detrimental effect of dissipation on the critical load for flutter is experimentally demonstrated. The introduced approach to follower forces discloses new horizons for testing self-oscillating structures and for exploring and documenting dynamic instabilities possible when nonconservative loads are applied.