The destabilizing effect of external damping: Singular flutter boundary for the Pfluger column with vanishing external dissipation

TL;DR

This paper reveals that external damping, contrary to traditional belief, can destabilize elastic structures under nonconservative forces, similar to internal damping, leading to a paradoxical reduction in flutter stability thresholds.

Contribution

It demonstrates that external damping can cause destabilization in elastic structures, correcting previous misconceptions and extending the destabilization paradox to external dissipation effects.

Findings

External damping destabilizes Pfluger and Ziegler's structures.

Destabilization effect is similar for internal and external damping.

Revised understanding of viscous damping's role in stability.

Abstract

Elastic structures loaded by nonconservative positional forces are prone to instabilities induced by dissipation: it is well-known in fact that internal viscous damping destabilizes the marginally stable Ziegler's pendulum and Pfluger column (of which the Beck's column is a special case), two structures loaded by a tangential follower force. The result is the so-called 'destabilization paradox', where the critical force for flutter instability decreases by an order of magnitude when the coefficient of internal damping becomes infinitesimally small. Until now external damping, such as that related to air drag, is believed to provide only a stabilizing effect, as one would intuitively expect. Contrary to this belief, it will be shown that the effect of external damping is qualitatively the same as the effect of internal damping, yielding a pronounced destabilization paradox. Previous results relative to destabilization by external damping of the Ziegler's and Pfluger's elastic structures are corrected in a definitive way leading to a new understanding of the destabilizating role played by viscous terms.