University of Cambridge > Talks.cam > Engineering Department Mechanics Colloquia Research Seminars > Snaking, dripping, and fluttering of elastic rods

Snaking, dripping, and fluttering of elastic rods

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The problem of an elastic rod deforming in a plane, namely the so-called ‘planar elastica’, has a long history, rooting to Jacob Bernoulli (1654-1705), Daniel Bernoulli (1700-1782), Leonhard Euler (1707-1783), and Pieter van Musschenbroek (1692-1761), but is still actual and rich of applications, sometimes unexpected. Using the elastica theory, configurational or ‘Eshelby-like’ forces are shown to arise in elastic structures when a change in configuration is possible, with a related release of energy. This concept has been developed theoretically and experimentally in a series of recent works involving: a clamped elastic rod forced to slip inside a sliding sleeve [1], the development of the so-called ‘elastica arm scale’ [2], the development of an elastica in the shape of a drop [3], an example of torsional locomotion [4] and serpentine motion within a smooth channel [5]. The dynamics of an elastic rod in a cantilever configuration and subject to a tangential follower load of the ‘Ziegler type’ at its end (the ‘Pfluger problem’) is finally addressed. This structure is subject to a Hopf bifurcation, corresponding to the initiation of the ‘flutter instability’. A new experimental set-up has been designed, produced and tested to realize the follower load. Experiments provide the evidence of flutter and divergence instability and provide the first proof that damping sources have a destabilizing effect on the system (the so-called ‘Ziegler paradox’).

From left to right: a snake in a rigid and frictionless channel, dripping and fluttering of an elastic rod

References [1] Bigoni, D, Bosi, F., Dal Corso, F. and Misseroni, D. (2014) Instability of a penetrating blade, J. Mech. Phys. Solids vol. 64, pp. 411–425. [2] Bosi, F., Dal Corso, F., Misseroni, D. and Bigoni, D. (2014) An Elastica Arm Scale, Proc. Royal Soc. A, 470, 20140232. [3] F. Bosi, D. Misseroni, F. Dal Corso, and D. Bigoni (2015) Self-encapsulation, or the ‘dripping’ of an elastic rod Proc. Royal Soc. A, vol. 471, 20150195. [4] Bigoni, D., Dal Corso, F., Misseroni, D. and Bosi, F. (2014) Torsional locomotion, Proc. Royal Soc. A, 470, 20140599. [5] Dal Corso, F., Misseroni, D., Pugno, N.M., Movchan, A.B., Movchan, N.V., Bigoni, D. (2017). Serpentine locomotion through elastic energy release. Journal of the Royal So

This talk is part of the Engineering Department Mechanics Colloquia Research Seminars series.

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