Abstract
AbstractWe consider the non‐linear two‐dimensional oscillations of a fluid conveying tube using dynamical bifurcation theory. The tube is clamped at the upper end, and at its free lower end a point mass is fixed. The tube is assumed to be slender and flexurally elastic, and its transversal motion is constrained by two symmetrically arranged springs. The flow rate of the incompressible fluid is used as a distinguished parameter in the problem. By determining the stability regions in parameter space, it is investigated whether Hopf and/or steady‐state bifurcations may occur, as it was found for similar cases in previous works [1,3]. The non‐linear behaviour close to the bifurcation points is analyzed. Of specific interest are low‐order resonances. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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