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A Double Pendulum in a Wind Field

The non-resonant case

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Abstract

In this paper an aeroelastic oscillator of a double pendulum type is studied by using a quasi-steady approach to model the flow-induced vibrations. The attention is focused to the analysis of the qualitive changes in the structure’s dynamics for increasing flow velocity. By making extensive use of computer algebra techniques new results have been obtained for the description of the so-called jump phenomenon in this system with two degrees of freedom.

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References

  1. W. W. Adams and P. Loustaunau, An introduction to Gröbner bases, American Mathematical Society, 1994.

    Google Scholar 

  2. R.D. Blevins, Flow induced vibration (2nd edition), Van Nostrand Reinhold, New York, 1990.

    Google Scholar 

  3. A.H.P. van der Burgh, Dynamical Systems as Models for Flow-induced Vibrations, Solitons, Chaos and Fractals, Vol. 5, No. 9, p. 1563–1577, 1995.

    Article  MATH  Google Scholar 

  4. A.H.P. van der Burgh, T.I. Haaker and B.W. van Oudheusden, A new aeroelastic oscillator, theory and experiments, DE-Vol. 84-1, 1995 Design Engineering Technical Conferences, Volume 3-Part A, ASME 1995.

    Google Scholar 

  5. H. Goldstein, Classical Mechanics, 2nd edition, Addison-Wesley Publishing Company, Inc., 1980.

    Google Scholar 

  6. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, New York, 1990.

    Google Scholar 

  7. T.I. Haaker and A.H.P. van der Burgh, On the dynamics of aeroelastic oscillators with one degree of freedom, SIAM J. Appl. Math., Vol.54 (1994), pp. 1033–1047.

    Article  MathSciNet  MATH  Google Scholar 

  8. T.I. Haaker, Dynamical behaviour of aeroelastic oscillators with one degree of freedom, Report 94-63, Faculty of Technical Mathematics and Informatics, Delft University of Technology, 1994.

    Google Scholar 

  9. T.I. Haaker, Quasi-steady modelling and asymptotic analysis of aeroelastic oscillators, Ph.D. Thesis, Department of Technical Mathematics and Computer Science, Delft University of Technology, Delft, 1996.

    Google Scholar 

  10. M.J. Huiskes, An aeroelastic oscillator with two degrees of freedom, M.Sc. Thesis, Department of Technical Mathematics and Computer Science, Delft University of Technology, Delft, 1996.

    Google Scholar 

  11. B. W. van Oudheusden, On the quasi-steady analysis of one-degree-of-freedom galloping with combined translational and rotational effects, Nonlinear Dynamics, Vol.8, no.2, September 1995.

    Google Scholar 

  12. B. W. van Oudheusden, Investigation of Large-Amplitude 1-DOF Rotational Galloping, Report LR-794, Faculty of Aerospace Engineering, Delft University of Technology, September 1995.

    Google Scholar 

  13. G. V. Parkinson and J. D. Smith, The square prism as an aeroelastic non-linear oscillator, Quart. J. Mech. and Appl Math., Vol.XVII (1964), Pt.2, pp. 225–239.

    Article  Google Scholar 

  14. J.A. Sanders and F. Verhulst, Averaging Methods in Nonlinear Dynamical Systems, AMS 59, Springer-Verlag, New-York, 1985.

    MATH  Google Scholar 

  15. L. A. Timochouk, Wagram: Yet another Gröbner system, in Numerical Analysis, Scientific Computing, Computer Science (Proceedings of the 3rd International Congress on Industrial and Applied Mathematics, Hamburg 3–7 July 1995), Ed. by G. Alefeld, Zeitschrift für Angewandte Mathematik undo Mechanik, Akademie Verlag, Berlin, (1996).

    Google Scholar 

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© 1997 Springer Science+Business Media Dordrecht

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Huiskes, M.J., Van der Burgh, A.H.P. (1997). A Double Pendulum in a Wind Field. In: van Groesen, E., Soewono, E. (eds) Differential Equations Theory, Numerics and Applications. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5157-3_17

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  • DOI: https://doi.org/10.1007/978-94-011-5157-3_17

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6168-1

  • Online ISBN: 978-94-011-5157-3

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