[Back]

A. Steindl:
"Resonance in the Hopf-Hopf interaction of a spatial fluid conveying tube";
Talk: ECCOMAS 2012 (European Congress on Computational Methods in Applied Sciences and Engineering, Wien; 2012-09-10 - 2012-09-14.

We investigate the spatial dynamics of a fluid conveying tube in the
vicinity of a multiple Hopf bifurcation with 1:3 resonance. The
rotational symmetry around the vertical axis forces all critical eigenvalues of the linearized dynamics to occur twice, leading to an
eight-dimensional system on the Centre Manifold. After reducing the
equations to Normal Form, thereby making use of the O(2)-symmetry, we can classify the hierarchy of primary and secondary solution branches. The presence of the resonance terms leads mode interactions, which behave similar to Duffing and nonlinear Mathieu equations, respectively.

Rotational Symmetry, Resonance, Hopf-Bifurcation