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. 2016 Oct;13(123):20160523. doi: 10.1098/rsif.2016.0523

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© 2016 The Author(s)

Published by the Royal Society. All rights reserved.

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Figure 2. — Well-known cases in which steady axial loading or flow leads to instability. (a) A compressive tip load with a fixed direction causes buckling (a static pitchfork bifurcation) when the force exceeds the critical value . (b,c) A compressive tip load that remains tangent to the beam (a non-conservative follower load) leads to oscillatory motion known as flutter, via a dynamic Hopf bifurcation, when the force exceeds a critical value (animation in electronic supplementary material, movie M1). (d) Flutter in a flexible tube conveying water. Instability occurs above a critical flow rate. Panel (d) is from Greenwald & Dugundji [30] reproduced with permission from Paidoussis [31]. (Online version in colour.)

Inline graphic — Well-known cases in which steady axial loading or flow leads to instability. (a) A compressive tip load with a fixed direction causes buckling (a static pitchfork bifurcation) when the force exceeds the critical value . (b,c) A compressive tip load that remains tangent to the beam (a non-conservative follower load) leads to oscillatory motion known as flutter, via a dynamic Hopf bifurcation, when the force exceeds a critical value (animation in electronic supplementary material, movie M1). (d) Flutter in a flexible tube conveying water. Instability occurs above a critical flow rate. Panel (d) is from Greenwald & Dugundji [30] reproduced with permission from Paidoussis [31]. (Online version in colour.)