Abstract
The three-dimensional mixed problem of the separation impact of a circular disk floating on the surface of an ideal incompressible unlimited fluid is considered. The position and shape of the contact area between the body and the fluid (and the separation zone) are not known and depend on the relation between the translational and angular velocities acquired by the disk upon impact. Because of this, the problem in question is nonlinear and belongs to the class of free-boundary problems. The problem is solved using the method of Hammerstein-type nonlinear boundary integral equations. This approach allows the fluid flow after impact and the unknown zone of separation of fluid particles to be determined simultaneously.
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References
L. I. Sedov, Two-dimensional Problems of Hydrodynamics and Aerodynamics [in Russian], Nauka, Moscow (1966).
N. A. Kudryavtseva, “Horizontal impact of a floating ellipse on an incompressible fluid,” Prikl. Mat. Mekh., 24, 258–261 (1960).
V. S. Korchagin, “Separation impact on a cylinder immersed in a fluid,” Izv. Sev.-Kavk. Nauch Tsentr. Vyssh. Shk., Estestv. Nauki, No. 4, 25–27 (1978).
V. S. Korchagin, “On separation impact of a body on an incompressible fluid,” Izv. Sev.-Kavk. Nauch Tsentr. Vyssh. Shk., Estestv. Nauki, No. 3, 30–33 (1989).
A. V. Dvorak and D. A. Teselkin, “Numerical study of two-dimensional problems of impulsive motion of floating bodies,” Zh. Vychisl. Mat. Mat. Fiz., 26, No. 1, 144–150 (1986).
M. V. Norkin, “Methods for solving nonlinear problems of hydrodynamic impact in bounded regions,” Izv. Ross. Akad. Nauk, Ser. Zhidk Gaza, No. 4, 135–147 (2005).
M. V. Norkin, “Separation impact of an elliptic cylinder floating on the surface of an ideal incompressible fluid of finite depth,” Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 1, 120–132 (2008).
M. A. Krasnosel’skii, G. M. Vainikko, P. P. Zabreiko, Ya. B. Rutitskii, and V. Ya. Stetsenko, Approximate Solution of Operator Equations [in Russian], Nauka, Moscow (1969).
B. A. Galanov, “Method of Hammerstein-type boundary equations for contact elastic problems with unknown contact areas,” Prikl. Mat. Mekh., 49, No. 5, 827–835 (1985).
V. M. Aleksandrov and D. A. Pozharskii, Nonclassical Two-Dimensional Problems of Mechanics of Contact Interactions of Elastic Solids [in Russian], Faktorial, Moscow (1998).
V. M. Aleksandrov and M. I. Chebakov, Analytical Methods in Contact Problems of Elastic Theory [in Russian], Fizmatlit, Moscow (2004).
V. I. Yudovich, “Unique solvability of the problem of separation impact of a solid on an inhomogeneous fluid,” Vladikavkaz. Mat. Zh., 7, No. 3, 79–91 (2005).
A. A. Korobkin, “Formulation of the penetration problem in the form of a variational inequality,” in: Dynamics of Continuous Media (collected scientific papers) [in Russian], No. 58, Inst. of Hydrodynamics, Sib. Div., USSR Acad. of Sci., Novosibirsk (1982), pp. 73–79.
I. I. Vorovich and V. I. Yudovich, “Impact of a circular disk on a fluid of finite depth,” Prikl. Mat. Mekh., 21, 525–532 (1957).
Ya. S. Uflyand, Method of Dual Equations in Problems of Mathematical Physics [in Russian], Nauka, Leningrad (1977).
A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series. Elementary Functions [in Russian], Nauka, Moscow (1981).
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 76–86, July–August, 2009.
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Norkin, M.V. Separation impact of a circular disk floating on the surface of an ideal incompressible fluid of infinite depth. J Appl Mech Tech Phy 50, 607–616 (2009). https://doi.org/10.1007/s10808-009-0082-2
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DOI: https://doi.org/10.1007/s10808-009-0082-2