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On the Parametric Excitation of a Nonlinear Aeroelastic Oscillator

[+] Author Affiliations
H. Lumbantobing, T. I. Haaker

Delft University of Technology, Delft, The Netherlands

Paper No. IMECE2002-32163, pp. 213-224; 12 pages
doi:10.1115/IMECE2002-32163
From:
  • ASME 2002 International Mechanical Engineering Congress and Exposition
  • 5th International Symposium on Fluid Structure Interaction, Aeroelasticity, and Flow Induced Vibration and Noise
  • New Orleans, Louisiana, USA, November 17–22, 2002
  • Conference Sponsors: Applied Mechanics Division
  • ISBN: 0-7918-3659-2 | eISBN: 0-7918-1691-5, 0-7918-1692-3, 0-7918-1693-1
  • Copyright © 2002 by ASME

abstract

In this paper the following equation for the parametric excitation of a nonlinear aeroelastic oscillator of seesaw type is considered:

θ̈ + 1 − εa0 cos(ωt) θ = εF(θ, θ̇, μ).
In this equation εF represents the aeroelastic force, μ the wind velocity and ε denotes a small parameter. To study the dynamics of the oscillator we use the method of averaging. In absence of parametric excitation one typically finds that above a critical wind velocity the oscillators rest position becomes unstable and stable oscillations with finite amplitude result. Addition of the parametric excitation changes this simple picture. On changing the wind velocity local bifurcations like pitchfork, saddle-node and Hopf bifurcations lead to new nontrivial critical points and limit cycles in the averaged equations. In addition, a global saddle-connection bifurcation is found which either creates or destroys a limit cycle. Note that critical points and limit cycles in the averaged system correspond to periodic solutions and periodically modulated solutions of the original system. An analysis for the possible stability diagrams of the trivial solution and the location of bifurcations in the parameter space is presented. Finally, the numerical calculations performed match with the obtained analytical results and provide phaseportraits for some especial cases.

Copyright © 2002 by ASME

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