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

Mirko Tommasini, Oleg Kirillov, Diego Misseroni, Davide Bigoni

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)
8 Downloads (Pure)

Abstract

Elastic structures loaded by non-conservative positional forces are prone to instabilities induced by dissipation: it is well-known that internal viscous damping destabilizes the marginally stable Ziegler's pendulum and Pflüger 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 Pflüger's elastic structures are corrected in a definitive way leading to a new understanding of the destabilizating role played by viscous terms.
Original languageEnglish
Pages (from-to)204-215
JournalJournal of the Mechanics and Physics of Solids
Volume91
Early online date17 Mar 2016
DOIs
Publication statusPublished - 1 Jun 2016

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