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IssuesArchive of Issues2008-1pp.146-152

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V. A. Samsonov and Yu. D. Selyutskii, "Comparison of different notation for equations of motion of a body in a medium flow," Mech. Solids. 43 (1), 146-152 (2008)
Year 2008 Volume 43 Number 1 Pages 146-152
DOI 10.3103/S0025654408010159
Title Comparison of different notation for equations of motion of a body in a medium flow
Author(s) V. A. Samsonov (Institute of Mechanics Lomonosov Moscow State University, Michurinskii pr-t 1, Moscow, 119192, Russia, samson@imec.msu.ru)
Yu. D. Selyutskii (Institute of Mechanics Lomonosov Moscow State University, Michurinskii pr-t 1, Moscow, 119192, Russia, seliytski@imec.msu.ru)
Abstract In [1-6], a model of a nonstationary action of a medium flow on a body moving in this flow was constructed in the form of an associated dynamical system of second order. In the literature, the representation of the aerodynamic force in integral form with a Duhamel type integral is often used (e.g., see [7, 8]). In the present paper, we pay attention to the fact that a system of ODE is equivalent not to a single integro-differential equation but to a family of such equations. Therefore, it is necessary to discuss the problem of the correspondence between their solutions. The integro-differential representation of the aerodynamic force is reduced to a form convenient to realize the procedure of separation of motions. In this case, we single out the first two approximations with respect to a small parameter. It turns out that in the case of actual airfoils one can speak of "detached" rather than "attached" mass.

In the problem on the forced drag of an airfoil in a flow, it is shown that for a sufficiently large acceleration the aerodynamic force can change its direction and turn from a drag force into an "accelerating" force for some time. At the same time, in the case of free drag of a sufficiently light plate, the "acceleration" effect is not observed, but in the course of deceleration the plate moves from it original position in the direction opposite to the initial direction of motion.
References
1.  V. A. Samsonov and Yu. D. Selyutskii, On the Possibility of Taking Account of the Inertial Properties of the Medium Acting on a Body (Izd-vo MGU, Moscow, 2000) [in Russian].
2.  Yu. D. Selyutskii, "On Inertial Properties of the Medium Acting on a Solid," in Theses of Intern. Conference "Modern Problems of Aeronautic Science and Technology". Zhukovskii-Moscow, May 23-26, 2000 (TsAGI, Moscow, 2000), p. 217 [in Russian].
3.  Yu. D. Selyutskii, Phenomenological Model of Taking Account of the Inertial Properties of the Medium Acting on a Solid, Candidateís Dissertation in Mathematics and Physics (Moscow, 2001).
4.  Yu. D. Selyutskii, "On Oscillations of a Plate in the Flow of Resisting Medium," in Proc. Conference-Competition of Young Scientists of Institute of Mechanics Lomonosov MSU. October 15-17, 2002. (Inst. Mech. MGU, Moscow, 2002), pp. 79-84 [in Russian].
5.  V. A. Samsonov and Yu. D. Selyutskii, "On the Problem of a Plate Oscillations in the Flow of a Resisting Medium," in Selected Proc. Intern. Conf. "Third Polyakhovís Readings" (Izd-vo St.Petersburg Univ., St. Petersburg, 2003), pp. 220-225 [in Russian].
6.  V. A. Samsonov and Yu. D. Selyutskii, "Vibration of a Plate in the Flow of a Resisting Medium," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 4, 24-31 (2004) [Mech. Solids (Engl. Transl.) 39 (4), 19-25 (2004)].
7.  S. M. Belotserkovskii, B. K. Skripach, and V. G. Tabachnikov, Wing in Unsteady Gas Flow (Nauka, Moscow, 1971) [in Russian].
8.  S. M. Belotserkovskii, Yu. A. Kochetkov, B. E. Loktev, and V. M. Tomshin, "Linear and Quasilinear Problems of Dynamics of a Rigid Apparatus with Moving Control Surfaces," Trudy VVIA im. Zhukovskogo, No. 132, 110-146 (1971).
9.  I. V. Novozhilov, Fractional Analysis (Izd-vo MGU, Moscow, 1995) [in Russian].
Received 03 February 2005
Link to Fulltext http://www.springerlink.com/content/1p6165rr41u4v32l
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