Flutter and divergence instability in the Pfluger column: experimental evidence of the Ziegler destabilization paradox

Abstract

Flutter instability in elastic structures subject to follower load, the most important cases being the famous Beck's and Pfluger'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 this field, the most important issue is the validation of the model itself of follower force, a nonconservative action which was harshly criticized and never realized in practice for structures with diffused elasticity. 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 flat surface (realized by a conveyor belt). It is therefore shown that follower forces can be realized in practice and the first experimental evidence is given for both the flutter and divergence instabilities occurring in the Pfluger's column. In particular, load thresholds for the two instabilities are measured and the detrimental effect of dissipation on the critical load for flutter is experimentally demonstrated, while a slight increase in load is found for the divergence instability. The presented 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.

arXiv comment28 pages, 12 figures

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• Flutter instability and Ziegler destabilization paradox for elastic rods subject to non-holonomic constraints
• Large deflections and stability of spring-hinged cantilever beam
• Fusion of two stable elastic structures resulting in an unstable system
• From rotating fluid masses and Ziegler's paradox to Pontryagin- and Krein spaces and bifurcation theory
• Feedback-Induced Flutter Instability of a Flexible Beam in Fluid Flow
• Finding the strongest stable weightless column with a follower load and relocatable concentrated masses
• A way to hypo-elastic artificial materials without a strain potential and displaying flutter instability