Gushing metal chain

doi:10.1007/s11465-016-0377-y

Front. Mech. Eng.

2016, Vol. 11

Issue (1) : 95-100 https://doi.org/10.1007/s11465-016-0377-y

RESEARCH ARTICLE

Gushing metal chain

Alexander BELYAEV, Alexander SUKHANOV(

), Alexander TSVETKOV

Institute of Applied Mathematics and Mechanics, Saint-Petersburg Polytechnic University, St. Petersburg 195251, Russia

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Abstract

This article addresses the problem in which a chain falls from a glass from some height. This phenomenon demonstrates a paradoxical rise of the chain over the glass. To explain this effect, an initial hypothesis and an appropriate theory are proposed for calculating the steady fall parameters of the chain. For this purpose, the modified Сayley ’s problem of falling chain given its rise due to the centrifugal force of upward inertia is solved. Results show that the lift caused by an increase in linear density at the part of chain where it is being bent (the upper part) is due to the convergence of the chain balls to one another. The experiments confirm the obtained estimates of the lifting chain.

Keywords chain fountain Meshchersky equation Cayley’s problem

Corresponding Author(s): Alexander SUKHANOV

Online First Date: 01 February 2016 Issue Date: 02 March 2016

Cite this article:

Alexander BELYAEV,Alexander SUKHANOV,Alexander TSVETKOV. Gushing metal chain[J]. Front. Mech. Eng., 2016, 11(1): 95-100.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-016-0377-y
https://academic.hep.com.cn/fme/EN/Y2016/V11/I1/95

Fig.1 Gushing chain

Fig.2 Steady-state behavior

Fig.3 Nonstationary problem of falling chain until it touches the floor

Fig.4 Nonstationary Cayley’s problem (1857)

Fig.5 Generalized Cayley’s problem

Fig.6 Straight and curved chain

Fig.7 The relative difference of linear density circuit

Fig.8 Experiment with inextensible flexible braid

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