Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

The singular perturbation limit of an elastic structure in a rapidly flowing nearly inviscid fluid


Authors: Zvi Artstein and Marshall Slemrod
Journal: Quart. Appl. Math. 59 (2001), 543-555
MSC: Primary 34C60; Secondary 34C29, 34E15, 74F10, 76B99
DOI: https://doi.org/10.1090/qam/1848534
MathSciNet review: MR1848534
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The effective forces that govern the vertical oscillations of an elastic structure in a horizontally flowing fluid are displayed for the limit case where fluid velocity and viscosity tend to singular limits. The derived singular perturbation model is based on available representations that model the coupled dynamics as coupled oscillators. The fast dynamics of the system does not, in general, converge on the fast time scale to a stationary point; thus, the classical singular perturbation methods are not applicable. Rather, a method based on Young measures representation of the fast oscillations, and on averaging, is employed.


References [Enhancements On Off] (What's this?)

  • [1] Z. Artstein and A. Vigodner, Singularly perturbed ordinary differential equations with dynamic limits, Proc. Royal Society Edinburgh 126A, 541-569 (1996) MR 1396278
  • [2] J. M. Ball, A version of the fundamental theorem for Young measures, in PDEs and Continuum Models of Phase Transitions, M. Rascle, D. Serre, and M. Slemrod, eds., Lecture Notes in Physics, 344, Springer-Verlag, Berlin-New York, 1988, pp. 207-215 MR 1036070
  • [3] Y. N. Chen, Fluctuating lift forces of the Kármán vortex streets on single circular cylinders and in tube bundles, Part 1, J. of Engineering for Industry, Trans. ASME 96, Ser. B, 603-612 (1972)
  • [4] E. H. Dowell and M. Ilgamov, Studies in Nonlinear Aeroelasticity, Springer-Verlag, New York, 1988 MR 957301
  • [5] W. D. Iwan and R. D. Belvins, A model for vortex induced oscillation of structure, J. Applied Mechanics 41, 581-586 (1974)
  • [6] Th. von Kármán, Über den Mechanismus des Flüssigkeitswiderstandes den ein bewegter Körper in einer Flüssigkeit erfährt, Nachrichten Königlichen Gesellschaft der Wissenschaften zu Göttingen, 1912, pp. 508-517
  • [7] N. E. Kochin, I. A. Kibel', and N. V. Roze, Theoretical Hydromechanics, John Wiley and Sons, New York, 1964 MR 0175414
  • [8] S. Lefschetz, Differential Equations: Geometric Theory, Dover, New York, 1977 MR 0435481
  • [9] V. V. Nemytskii and V. V. Stepanov, Qualitative Theory of Differential Equations, Princeton University Press, Princeton, 1960 MR 0121520
  • [10] R. E. O'Malley, Jr., Singular Perturbation Methods of Ordinary Differential Equations, Springer-Verlag, New York, 1991

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 34C60, 34C29, 34E15, 74F10, 76B99

Retrieve articles in all journals with MSC: 34C60, 34C29, 34E15, 74F10, 76B99


Additional Information

DOI: https://doi.org/10.1090/qam/1848534
Article copyright: © Copyright 2001 American Mathematical Society

American Mathematical Society