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Mode interactions and resonances of an elastic fluid‐conveying tube
Author(s) -
Jurisits Richard,
Steindl Alois
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110153
Subject(s) - bifurcation , parameter space , tube (container) , compressibility , physics , mechanics , hopf bifurcation , bifurcation theory , space (punctuation) , flow (mathematics) , linear stability , steady state (chemistry) , transversal (combinatorics) , stability (learning theory) , pitchfork bifurcation , classical mechanics , mathematics , mathematical analysis , materials science , geometry , nonlinear system , chemistry , instability , linguistics , philosophy , quantum mechanics , machine learning , computer science , composite material
We 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)