, Volume 48, Issue 9, pp 1258-1271

Landau-Hopf scenario of passage to turbulence in some problems of elastic stability theory

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Abstract

We consider a boundary value problem for a nonlinear integro-differential equation modeling the vibrations of a pipe transporting a fluid and the vibrations of a thin cylinder in an axisymmetric flow. For the boundary conditions we take the hinge support conditions. We show that the Landau-Hopf scenario of passage to turbulence can be realized in such a problem, whereby stable invariant tori of increasing dimensions are generated as the main bifurcation parameter increases.

Original Russian Text © A.N. Kulikov, 2012, published in Differentsial’nye Uravneniya, 2012, Vol. 48, No. 9, pp. 1278–1291.