Abstract
The loss of stability of the trivial downhanging equilibrium position of a slender circular tube conveying incompressible fluid flow is studied. The tube is clamped at its upper end and free at its lower end. Inbetween the three-dimensional transversal motion is constrained by an elastic support which is considered to be D 4-symmetric, that is, has the symmetry of the square (Figure 1). Kirchhoff’s rod theory and the Kelvin-Voigt viscoelastic law are used to derive the tube equations under the assumption of large displacement but small strain.
The stability analysis is performed making use of the methods of equivariant bifurcation theory, that is, making use of the symmetry properties of the original system in deriving the amplitude equations of the critical modes. All cases of loss of stability which are possible for generic one-parameter bifurcations and the coincident case of a zero root and a purely imaginary pair of roots are investigated.
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Steindl, A., Troger, H. (1995). One and Two-Parameter Bifurcations to Divergence and Flutter in the Three-Dimensional Motions of a Fluid Conveying Viscoelastic Tube with D4-Symmetry. In: Bajaj, A.K., Shaw, S.W. (eds) Advances in Nonlinear Dynamics: Methods and Applications. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0367-1_8
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DOI: https://doi.org/10.1007/978-94-011-0367-1_8
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