On an unduly simplified model in the non-conservative problems of elastic stability

Sugiyama, Yoshihiko; Kashima, Kenji; Kawagoe, Haruo

doi:10.1016/0022-460x(76)90598-8

Cited by 15 publications

(15 citation statements)

References 7 publications

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“…9. This behaviour was previously analyzed by Sugiyama et al (1976), Pedersen (1977), Chen & Ku (1992), and Ryu & Sugiyama (2003), but only theoretically and without considering external and internal damping separately. Experiments, and therefore also theoretical predictions, are reported in Fig.…”

Section: Onset Of Flutter and Divergence In The Presence Of Internal mentioning

confidence: 99%

Flutter and divergence instability in the Pflüger column: Experimental evidence of the Ziegler destabilization paradox

Bigoni

Kirillov

Misseroni

et al. 2018

Journal of the Mechanics and Physics of Solids

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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 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 Pflüger'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.

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Section: Onset Of Flutter and Divergence In The Presence Of Internal mentioning

confidence: 99%

Flutter and divergence instability in the Pflüger column: Experimental evidence of the Ziegler destabilization paradox

Bigoni

Kirillov

Misseroni

et al. 2018

Journal of the Mechanics and Physics of Solids

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“…Often, the underlying physical problem (if any) has been oversimpli"ed [7]. But still, many of these studies are very interesting from a general theory of dynamic stability point of view, and studies of simple follower force systems help to obtain a deeper understanding of much more complex practical/industrial stability problems.…”

Section: Models Considered In This Papermentioning

confidence: 98%

Dynamic Stability of Columns Subjected to Follower Loads: A Survey

Langthjem

Sugiyama

2000

Journal of Sound and Vibration

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190

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“…These values, corresponding to two extreme situations, are connected by a marginal stability curve in the (p, α)-plane that was numerically evaluated in (Pflüger, 1955;Bolotin, 1963;Oran, 1972;Sugiyama et al, 1976;Pedersen, 1977;Ryu and Sugiyama, 2003). The instability threshold of the undamped Pflüger column is shown in Fig.…”

Section: Ziegler's Paradox For the Pflüger Column With External Dampingmentioning

confidence: 99%

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

Tommasini

Kirillov

Misseroni

et al. 2016

Journal of the Mechanics and Physics of Solids

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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 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.

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On an unduly simplified model in the non-conservative problems of elastic stability

Cited by 15 publications

References 7 publications

Flutter and divergence instability in the Pflüger column: Experimental evidence of the Ziegler destabilization paradox

Flutter and divergence instability in the Pflüger column: Experimental evidence of the Ziegler destabilization paradox

Dynamic Stability of Columns Subjected to Follower Loads: A Survey

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

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