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

TL;DR

This paper presents an experimental setup demonstrating follower forces in elastic structures, providing evidence of flutter and divergence instabilities in Pfluger's column, and explores the effects of dissipation on these instabilities.

Contribution

It introduces a practical method to realize follower forces using Coulomb friction, experimentally validates flutter and divergence in Pfluger's column, and analyzes the impact of dissipation.

Findings

Follower forces can be practically realized using Coulomb friction.

Experimental evidence of flutter and divergence instabilities in Pfluger's column.

Dissipation reduces the critical load for flutter but slightly increases it for divergence.

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.