Abstract
The oscillations of a rigid body on an elastic tie (vibrator) in an ideal incompressible fluid with a free boundary, on which surface tension forces act, are considered. The linearized problem of hydrodynamics is solved approximately in the self-consistent formulation, the reaction forces exerted on the body by the fluid are calculated, and an integrodifferential equation of motion is obtained. Using asymptotic methods, the average characteristics determining the damping coefficient and the frequency shift of the oscillations of the vibrator are obtained with allowance for the effect of the capillary waves radiated by the vibrator. Qualitative effects depending on the parameters of the system are revealed. The authors' numerical simulation of the motion of the vibrator completely confirms the qualitative conclusions concerning the nature of the oscillations of a body in a fluid having surface tension.
Similar content being viewed by others
References
L. N. Sretenskii,Theory of Wave Motions of Fluids [in Russian], Nauka, Moscow (1977).
M. D. Khaskind,Hydrodynamic Theory of Ship Motion [in Russian], Nauka, Moscow (1973).
L. D. Akulenko, S. A. Mikhailov, S. V. Nesterov, and A. A. Chaikovskii, “Numerical-analytical study of oscillations of a rigid body at the interface between two fluids,”Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 4, 59 (1988).
L. D. Akulenko, S. A. Mikhailov, and S. V. Nesterov, “Oscillations of a vibrator in the neighborhood of the interface between two fluids,”Prikl. Mat. Mekh.,54, 40 (1990).
L. D. Akulenko, S. A. Mikhailov, and S. V. Nesterov, “Investigation of the dependence of the oscillations of a float on its surface shape in an inhomogeneous fluid,”Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 5, 24 (1990).
L. D. Akulenko and S. V. Nesterov, “Displacement of a vibrator beneath the surface of a heavy fluid,”Izv. Ros. Akad. Nauk, Mekh. Tverd. Tela, No. 4, 39 (1994).
H. Lamb,Hydrodynamics, Cambridge University Press, New York (1957).
Additional information
Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 126–132, March–April, 1995.
Rights and permissions
About this article
Cite this article
Akulenko, L.D., Korneev, S.V. & Nesterov, S.V. Effect of capillary wave radiation on the oscillations of a vibrator. Fluid Dyn 30, 261–266 (1995). https://doi.org/10.1007/BF02029839
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02029839