Abstract
The process of a fluid flow in an elastic pipeline with fixed ends is considered. It is shown that in such a pipeline auto-oscillations of the wall and the fluid stream or flutter of the skin mode can take place. A solution of the system of nonlinear hydrodynamical equations describing these auto-oscillations in elementary functions is presented. It is shown that standing waves in an elastic pipeline arise not due to the summation of direct and returning waves.
Similar content being viewed by others
REFERENCES
J. M. T. Thompson, Instabilities and Catastrophes in Science and Engineering (Wiley, Chichester, New York, 1982).
G. B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974).
B. M. Budak, A. A. Samarski, and A. N. Tikhonov, Collection of Problems in Mathematical Physics (Nauka, Moscow, 1980), pp. 14, 160 [in Russian].
A. N. Matveev, Molecular Physics (Vyssh. Shkola, Moscow, 1981) [in Russian].
A. N. Volobuev, Basis of Nonsymmetrical Hydrodynamics (Nova Science, New York, 2012; SamLyuks-Print, Samara, 2011).
V. I. Feodosev, Strength of Materials (Nauka, Moscow, 1986), p. 275 [in Russian].
C. G. Caro, T. J. Pedley, R. C. Schroter, and W. A. Seed, The Mechanics of the Circulation (Oxford Univ. Press, Oxford, 1978).
V. A. Krasilnikov and V. V. Krylov, Introduction to Physical Acoustics (Nauka, Moscow, 1984) [in Russian].
A. N. Tikhonov and A. A. Samarski, Equations of Mathematical Physics (Nauka, Moscow, 1972; Dover, New York, 2011).
G. M. Fikhtengolts, Differential and Integral Calculus Course (Fizmatgiz, Moscow, 1952), Vol. 1.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The authors declare that they have no conflicts of interest.
Rights and permissions
About this article
Cite this article
Volobuev, A.N. Nonlinear Features of a Fluid Flow in an Elastic Pipeline. Math Models Comput Simul 12, 53–59 (2020). https://doi.org/10.1134/S2070048220010093
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S2070048220010093