The aerodynamic instability of a suspended cable is studied by means of a reduced 2 d.o.f. planar model in the viewpoint of the bifurcation theory, by considering a family of systems unfolded by a number of parameters equal to the codimension of the problem. In particular, starting from the condition of perfect 1:1 internal resonance between the in-plane symmetric and anti-symmetric mode, a perturbation analysis of the nonlinear problem is performed and an explicit expression of the coefficients of the discrete equations of motion, in terms of the unfolding parameters, is obtained. In this way, the neighborhood of the first bifurcation point is analyzed, evaluating the actual extension of the instability regions and the chance of existence of quasi-periodic motions.
Bimodal planar galloping of suspended cables in 1:1 internal resonance
PICCARDO, GIUSEPPE
2008-01-01
Abstract
The aerodynamic instability of a suspended cable is studied by means of a reduced 2 d.o.f. planar model in the viewpoint of the bifurcation theory, by considering a family of systems unfolded by a number of parameters equal to the codimension of the problem. In particular, starting from the condition of perfect 1:1 internal resonance between the in-plane symmetric and anti-symmetric mode, a perturbation analysis of the nonlinear problem is performed and an explicit expression of the coefficients of the discrete equations of motion, in terms of the unfolding parameters, is obtained. In this way, the neighborhood of the first bifurcation point is analyzed, evaluating the actual extension of the instability regions and the chance of existence of quasi-periodic motions.
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