The Elastochrone: the descent time of a sphere on a flexible beam

Abstract : We present the results of a combined experimental and theoretical investigation of the motion of a sphere on an inclined flexible beam. A theoretical model based on Euler-Bernoulli beam theory is developed to describe the dynamics, and in the limit where the beam reacts instantaneously to the loading, we obtain exact solutions for the load trajectory and descent time. For the case of an initially horizontal beam, we calculate the period of the resulting oscillations. Theoretical predictions compare favourably with our experimental observations in this quasi-static regime. The time taken for descent along an elastic beam, the elastochrone, is shown to exceed the classical brachistochrone, the shortest time between two points in a gravitational field.
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Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, The, 2009, 465 (2107), pp.2293-2311. 〈10.1098/rspa.2009.0048〉
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Soumis le : vendredi 18 juillet 2014 - 10:28:02
Dernière modification le : jeudi 10 mai 2018 - 02:03:35

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Jeffrey Aristoff, Christophe Clanet, John Bush. The Elastochrone: the descent time of a sphere on a flexible beam. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, The, 2009, 465 (2107), pp.2293-2311. 〈10.1098/rspa.2009.0048〉. 〈hal-01025601〉

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