Skip to main content
SpringerLink
Log in

Oscillations of a membrane that is orthogonal to a flow: Asymptotics of large stresses

  • Published:
Journal of Soviet Mathematics Aims and scope Submit manuscript

Abstract

The problem of small free oscillations of a membrane that is orthogonal to an inflowing stream is considered. A quasi-cavitation numerical hydrodynamic scheme is used that combines the assumptions on the potential character of the flow before the membrane and the assumption of a constant bottom pressure. The problem is reduced to a homogeneous system of integral-differential and singular integral equations with respect to variables that give the form of the membrane and density of associated whirls. For a small velocity pressure an analytic solution to the problem in the first order of the perturbation theory is constructed. Analytic and numerical solutions to the problem are compared, which are obtained by using the methods of finite differences and “discrete” whirls.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Yu. A. Shevlyakov, V. N. Tishchenko, and V. A. Temnenko, Dynamics of Parachute Systems [in Russian], Vishcha Shk., Golovnoe Izd., Kiev, Odessa (1985).

    Google Scholar 

  2. A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  3. S. M. Belotserkovskii and M. I. Nisht, Separated and Nonseparated Streamline Flow of Thin Foils by an Ideal Fluid [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  4. L. I. Sedov, Mechanics of Continuous Media [in Russian], Vol. 2, Nauka, Moscow (1970).

    Google Scholar 

  5. A. H. Nayfeh, Introduction to Perturbation Techniques, Wiley, New York-Toronto (1981).

    Google Scholar 

  6. F. D. Gakhov, Boundary Problems [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  7. L. G. Loitsyanskii, Fluid and Gas Mechanics [in Russian], Nauka, Moscow (1970).

    Google Scholar 

  8. P. Chzhen, Separated Flows [Russian translation], Vol. 2, Mir, Moscow (1972).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Simferopol' University, USSR

    A. V. Il'chenko & V. A. Temnenko

Authors
  1. A. V. Il'chenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. A. Temnenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Dinamicheskie Sistemy, No. 7, pp. 41–47, 1988.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Il'chenko, A.V., Temnenko, V.A. Oscillations of a membrane that is orthogonal to a flow: Asymptotics of large stresses. J Math Sci 65, 1521–1525 (1993). https://doi.org/10.1007/BF01097656

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01097656

Keywords

Search

Navigation