Numerical Investigation of the Hopf-Bogdanov-Takens Mode Interaction for a Fluid-conveying Tube. (2017)

• Record Type: Journal Article
• Authors: Steindl, Alois
• Is Part Of: Procedia engineering. Volume 199(2017)
• Page Start: 857
• Page End: 862
• Publication Date: 2017
• Subjects: Fluid-conveying tube -- Hopf bifurcation -- Takens-Bogdanov bifurcation -- Mode interaction -- continuation method -- Shilnikov szenario 2000 MSC: 34C23 -- 34C25 -- 34C37 -- 37G10 -- 37G15 -- 37G20; Engineering -- Congresses; Engineering -- Periodicals; Engineering; Conference proceedings; Periodicals; 620.005
• DOI: 10.1016/j.proeng.2017.09.024
• Languages: English
• ISSNs: 1877-7058

Abstract

Abstract: We investigate the dynamics after loss of stability of the downhanging configuration of a fluid conveying tube with a small end mass and an elastic support. By varying the fluid flow rate and the stiffness and location of the elastic support, different degenerate bifurcation scenarios can be observed. In this talk we investigate the bifurcating solution branches of the codimension 3 interaction between a Hopf bifurcation and a Takens-Bogdanov bifurcation. An elaboratory discussion of the primary and secondary solution branches was already given by Langford and Zhan. After reducing the system to the three-dimensional Normal Form equations we apply a numerical continuation procedure to locate the expected higher order bifurcation branches and possibly detect more complicated dynamics, like Shilnikov orbits.