Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
Volume 37, Issue 4, Pages 1241-1250Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0305-4470/37/4/012
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We study a system of equations with fractional derivatives, that arises in the analysis of the lateral motion of an elastic column fixed at one end and loaded by a concentrated follower force at the other end. We assume that the column is positioned on a viscoelastic foundation described by a constitutive equation of fractional derivative type. The stability boundary is determined. It is shown that as in the case of an elastic (Winkler) type of foundation the stability boundary remains the same as for the column without a foundation! Thus, with the solution analysed here, the column exhibits the so-called Hermann-Smith paradox.
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