Abstract
The aeroelastic behavior of a planar prismatic visco-elastic structure, subject to a turbulent wind, flowing orthogonally to its plane, is studied in the nonlinear field. The steady component of wind is responsible for a Hopf bifurcation occurring at a threshold critical value; the turbulent component, which is assumed to be a small harmonic perturbation of the former, is responsible for parametric excitation. The interaction between the two bifurcations is studied in a three-dimensional parameter space, made of the two wind amplitudes and the frequency of the turbulence. Aeroelastic forces are computed by the quasi-static theory. A one-D.O.F dynamical system, drawn by a Galerkin projection of the continuous model, is adopted. The multiple scale method is applied, to get a two-dimensional bifurcation equation. A linear stability analysis is carried out to determine the loci of periodic and quasi-periodic bifurcations. Limit cycles and tori are computed by exact, asymptotic, and numerical solutions of the bifurcation equations. Numerical results are obtained for a sample structure, and compared with finite-difference solutions of the original partial differential equation of motion.
Highlights
The study of the aeroelastic behavior of slender structures is a fascinating topic, of high scientific and technical value
Nonautonomous systems, as structures subjected to turbulent wind, are prone to parametric excitation phenomena, leading to divergence, flip and Neimark–Sacker bifurcations
Quasi-periodic motions are found as limit cycles for the bifurcation equations, via a perturbation analysis
Summary
The study of the aeroelastic behavior of slender structures is a fascinating topic, of high scientific and technical value. The multiple scale method is used to study the effect of primary and secondary resonances on the galloping response of the structure Starting from this last work, the parametric, external, and self-excitation of one/two towers under turbulent wind flow is studied in [35,36,39] and in [37,38], focusing the attention to the periodic and quasi-periodic galloping motions. The investigation, mainly carried out by perturbation methods, is aimed at evaluating: (a) as the turbulent component reduces the galloping critical velocity, and vice versa, (b) as the steady wind component modifies the parametric excitation instability domain.
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