In this article we are dealing with a uniform cylindrical pole fixed in a vertical direction at its lowest point, and carried to such a height that the vertical position becomes unstable and flexure begins. Simultaneously the wind is assumed to blow so that being active as a transverse load, and the relevant elastica is investigated. The consequent nonlinear differential equation cannot be treated analytically: but its linearized variant, small deflections, can. We have been led to a Airy type equation to be integrated in closed form through the first kind Bessel and the 1F2 generalized hypergeometric functions. The problem has then completely solved: so we make a useful thing for engineering purposes, or better, for testing the relevant numerical algorithms.

A thin heavy flagpole bent under a transverse wind: his elastica by hypergeometric functions

MINGARI SCARPELLO, GIOVANNI;RITELLI, DANIELE
2012

Abstract

In this article we are dealing with a uniform cylindrical pole fixed in a vertical direction at its lowest point, and carried to such a height that the vertical position becomes unstable and flexure begins. Simultaneously the wind is assumed to blow so that being active as a transverse load, and the relevant elastica is investigated. The consequent nonlinear differential equation cannot be treated analytically: but its linearized variant, small deflections, can. We have been led to a Airy type equation to be integrated in closed form through the first kind Bessel and the 1F2 generalized hypergeometric functions. The problem has then completely solved: so we make a useful thing for engineering purposes, or better, for testing the relevant numerical algorithms.
Mingari Scarpello G.; Ritelli D.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/112740
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