| 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.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. |
