Advertisement

Czechoslovak Journal of Physics

, Volume 54, Issue 4, pp 413–421 | Cite as

Approximate analytical solution of the inhomogeneous Burgers equation

  • P. Koníček
  • M. Bednařík
Article
  • 44 Downloads

Abstract

The method of the active second harmonic suppression in resonators is investigated in this paper both analytically and numerically. The resonator is driven by a piston which vibrates with two frequencies. The first one agrees with an eigenfrequency and the second one is equal to the two times higher eigenfrequency. The phase shift of the second piston motion is 180 degrees. It is known that for this case it is possible to describe generation of the higher harmonics by means of the inhomogeneous Burgers equation. The new approximate solution of inhomogeneous Burgers equation for real fluid is presented here.

PACS

43.20.Ks 43.25.Jh 

Key words

inhomegeneous Burgers equation nonlinear standing waves Van Dyke matching principle 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    G.W. Swift: J. Acoust. Soc. Am.84 (1988) 1145.CrossRefADSGoogle Scholar
  2. [2]
    Yu.A. Illinski, B. Lipkens, T.S. Lucas, T.W. Van Doren, and E. Zabolotskaya: J. Acoust. Soc. Am.104 (1998) 2664.CrossRefADSGoogle Scholar
  3. [3]
    W. Chester: Proc. R. Soc. Lond. A444 (1994) 591.zbMATHADSCrossRefGoogle Scholar
  4. [4]
    H. Ockendon, J.R. Ockendon, M.R. Peake, and W. Chester: J. Fluid Mech.257 (1993) 201.zbMATHCrossRefADSMathSciNetGoogle Scholar
  5. [5]
    M.F. Hamilton, Y.A. Ilinskii, and E.A. Zabolotskaya: J. Acoust. Soc. Am.110 (2001) 109.CrossRefADSGoogle Scholar
  6. [6]
    Y.D. Chun and Y.H. Kim: J. Acoust. Soc. Am.108 (2000) 2765.CrossRefADSGoogle Scholar
  7. [7]
    V.G. Andreev, V.E. Gusev, A.A. Karabutov, O.V. Rudenko, and O.A. Sapozhnikov: Sov. Phys. Acoust.31 (1985) 162.Google Scholar
  8. [8]
    P.T. Huang and J.G. Brisson: J. Acoust. Soc. Am.102 (1997) 3256.CrossRefADSGoogle Scholar
  9. [9]
    V.E. Gusev, H. Bailliet, P. Lotton, S. Job, and M. Bruneau: J. Acoust. Soc. Am.103 (1998) 3717.CrossRefADSGoogle Scholar
  10. [10]
    N. Sugimoto, M. Masuda, T.H. Doi, and T. Doi: J. Acoust. Soc. Am.110 (2001) 2263.CrossRefADSGoogle Scholar
  11. [11]
    A.A. Atchley and D.F. Gaitan: J. Acoust. Soc. Am.93 (1993) 2489.CrossRefADSGoogle Scholar
  12. [12]
    V. Kaner, O.V. Rudenko, and R. Khokhlov: Sov. Phys. Acoust.23 (1977) 432.Google Scholar
  13. [13]
    V.E. Gusev: Sov. Phys. Acoust.30 (1984) 121.Google Scholar
  14. [14]
    M. Ochmann: J. Acoust. Soc. Am.77 (1985) 61.zbMATHCrossRefADSMathSciNetGoogle Scholar
  15. [15]
    D.B. Cruishank: J. Acoust. Soc. Am.52 (1972) 1024.CrossRefADSGoogle Scholar
  16. [16]
    C. Lawrenson, B. Lipkens, T.S. Lucas, D.K. Perkins, and T.W. Van Doren: J. Acoust. Soc. Am.104 (1998) 623.CrossRefADSGoogle Scholar
  17. [17]
    V.P. Kuznetsov: Sov. Phys. Acoust.16 (1971) 467.Google Scholar
  18. [18]
    M.F. Hamilton and D.T. Blackstock:Nonlinear Acoustic, Academic Press, San Diego, 1998.Google Scholar
  19. [19]
    A.H. Nayfeh:Perturbation Methods, John Wiley & Sons, New York, 1973.zbMATHGoogle Scholar
  20. [20]
    M. Van Dyke:Perturbation Methods in Fluid Mechanics, The Parabolic Press, Stanford, 1975.zbMATHGoogle Scholar

Copyright information

© Springer 2004

Authors and Affiliations

  • P. Koníček
    • 1
  • M. Bednařík
    • 1
  1. 1.Department of Physics, Faculty of Electro EngineeringCzech Technical UniversityPraha 6Czech Republic

Personalised recommendations