Nonlinear interaction between self- and parametrically excited wind-induced vibrations
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ORIGINAL PAPER
Nonlinear interaction between self- and parametrically excited wind-induced vibrations Simona Di Nino
· Angelo Luongo
Received: 2 June 2020 / Accepted: 23 November 2020 © The Author(s) 2020
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 quasistatic 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 com-
S. Di Nino · A. Luongo (B) Department of Civil, Construction-Architectural and Environmental Engineering, University of L’Aquila, 67100 L’Aquila, Italy e-mail: [email protected] S. Di Nino · A. Luongo International Research Center on Mathematics and Mechanics of Complex Systems, University of L’Aquila, 67100 L’Aquila, Italy
pared with finite-difference solutions of the original partial differential equation of motion. Keywords Aeroelstic system · Flip bifurcation · Neimark–Sacker bifurcation · Turbulent wind · Perturbation analysis
1 Introduction The study of the aeroelastic behavior of slender structures is a fascinating topic, of high scientific and technical value. The literature is rich of studies concerning specific flexible structures (cables [1–7], beams [8– 12], plates [13–16]) and general aeroelastic phenomena (galloping [17–21], flutter [22–25], vortex-induced vibrations (VIV) [26–30]). The instability and bifurcation events can be related to different kinds of excitation. Self-excited autonomous systems, as structures subjected to steady wind, are prone to Hopf bifurcations, caused by zeroing of the total damping. Nonautonomous systems, as structures subjected to turbulent wind, are prone to parametric excitation phenomena, leading to divergence, flip and Neimark–Sacker bifurcations. Depending on the nature of the loads, the different kinds of excitation can interact. Some attention has been devoted in literature to interactive aeroelastic phenomena, as galloping parametric excitation [31–40] or galloping vortex-induced vibrations [41– 45]. In particular, as regard the former class, the principal resonance of a single-degree-of-freedom system
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with two-frequency parame
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