Abstract
It is well known that a periodic change in the equilibrium or flow parameters of an incompressible liquid exerts a material influence on the hydrodynamic stability. As an example we may quote the parametric excitation of surface waves (gravitational-capillary [1], electrohydrodynamic [2], magnetohydrodynamic [3]) and the oscillations of liquid in communicating vessels [4, 5]. The chief object of the foregoing experimental investigations was that of determining the boundaries of the regions of unstable equilibrium with respect to small perturbations. In the present investigation we made an experimental study of the parametric resonance and finite-amplitude parametric oscillations arising in a liquid-filled U-tube subject to alternating vertical overloadings. We shall describe two forms of oscillations in the liquid, and we shall determine the corresponding ranges of unstable equilibrium with respect to small random perturbations (self-excitation) and also to finite-amplitude perturbations. We shall study nonlinear modes of excitation and mutual transitions between the two forms of oscillations. We shall find the ranges of existence of steady-state oscillations.
Similar content being viewed by others
Literature cited
J. W. Strutt (Rayleigh), Theory of Sound, Vols. 1 and 2, Dover (1937).
V. A. Briskman, and G. F. Shaidurov, “Parametric instability of a liquid surface in an alternating electric field,” Dokl. Akad. Nauk SSSR,180, No. 6 (1968).
V. A. Briskman and G. F. Shaidurov, “Parametric excitation of liquid instability in magnetic and electric fields,” Magnitn. Gidrodinamika, No. 3 (1969).
S. S. Grigoryan, L. I. Zhigachev, B. S. Kogarko, and Yu. L. Yakimov, “Parametric resonance in communicating vessels subject to variable vertical overloads,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 2 (1969).
V. A. Briskman, A. A. Ivanova, A. A. Cherepanov, and G. F. Shaidurov, “Parametric instability of the equilibrium of a liquid in communicating vessels,” in: Hydrodynamics, Scientific Proceedings of Perm University [in Russian], No. 8 (362) (1976).
N. K. Adam, Physics and Chemistry of Surfaces, 3rd ed., Dover (1969).
L. D. Landau and E. M. Lifshits, Mechanics of Continuous Media [in Russian], Gostekhizdat, Moscow (1953).
C. Clarion, “Oscillatory motion with viscosity and inertia,” Publs. Sci. Tech. Minstr. 1'Air, No. 303 (1955).
A. E. Kravchenko and A. G. Smirnov, “Experimental studies of the free attenuating oscillations of liquid in round U tubes,” in: Physical Hydrodynamics and Kinetics of Liquids [in Russian], Rostov-on-Don (1968).
A. Tondl, Nonlinear Vibrations of Mechanical Systems [Russian translation], Mir, Moscow (1973).
Author information
Authors and Affiliations
Additional information
Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 36–42, March–April, 1976.
The authors wish to thank G. I. Petrova and the participants in his seminar for useful discussions, and S. S. Grigoryan for valuable advice.
Rights and permissions
About this article
Cite this article
Briskman, V.A., Ivanova, A.A. & Shaidurov, G.F. Parametric oscillations of liquid in communicating vessels. Fluid Dyn 11, 206–212 (1976). https://doi.org/10.1007/BF01017381
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01017381