Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
 Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936

Russian Russian English English About Journal | Issues | Guidelines | Editorial Board | Contact Us
 


IPMech RASWeb hosting is provided
by the Ishlinsky Institute for
Problems in Mechanics
of the Russian
Academy of Sciences
IssuesArchive of Issues2016-6pp.632-642

Archive of Issues

Total articles in the database: 9179
In Russian (. . ): 6485
In English (Mech. Solids): 2694

<< Previous article | Volume 51, Issue 6 / 2016 | Next article >>
M.V. Belichenko, "Stability of High-Frequency Periodic Motions of a Heavy Rigid Body with a Horizontally Vibrating Suspension Point," Mech. Solids. 51 (6), 632-642 (2016)
Year 2016 Volume 51 Number 6 Pages 632-642
DOI 10.3103/S0025654416060029
Title Stability of High-Frequency Periodic Motions of a Heavy Rigid Body with a Horizontally Vibrating Suspension Point
Author(s) M.V. Belichenko (Moscow Aviation Institute (National Research University), Volokolamskoe sh. 4, Moscow, 125993 Russia, tuzemec1@rambler.ru)
Abstract The motion of a heavy rigid body one of whose points (the suspension point) executes horizontal harmonic high-frequency vibrations with small amplitude is considered. The problem of existence of high-frequency periodic motions with period equal to the period of the suspension point vibrations is considered. The stability conditions for the revealed motions are obtained in the linear approximation. The following three special cases of mass distribution in the body are considered; a body whose center of mass lies on the principal axis of inertia, a body whose center of mass lies in the principal plane of inertia, and a dynamically symmetric body.
Keywords rigid body, fast vibration, periodic motion, stability
References
1.  A. Stephenson, "On a New Type of Dynamical Stability," Mem. Proc. Manch. Lit. Phil. Soc. 52, Pt. 2 (8), 1-10 (1908).
2.  A. Stephenson, "On Induced Stability," Phil. Mag. Ser. 7 17, 765-766 (1909).
3.  S. S. Arutyunov, "On Damped Pendulum with Vibrating Suspension Point," Trudy Kazan. Aviats. Inst., No. 45, 93-102 (1959).
4.  P. Hirtsh, "Das Pendel mit Oszillierendem Aufhängepunkt," ZAMM 10 (1), 41-52 (1930).
5.  K. Klotter and G. Kotowski, "Über die Stabilität der Bewegungen des Pendels mit Oszillierendem Aufhängepunkt," ZAMM 19 (5), 289-296 (1939).
6.  P. L. Kapitsa, "Pendulum with Vibrating Suspension," Uspekhi Fiz. Nauk 44 (1), 7-20 (1951).
7.  P. L. Kapitsa, "Dynamical Stability of a Pendulum with Vibrating Suspension Point," Zh. Éksp. Teor. Fiz. 21 (5), 588-597 (1951).
8.  A. Erdélyi, "Über die Kleinen Schwingungen eines Pendels mit Oszillierendem Aufhängepunkt," ZAMM 14 (4), 235-247 (1934).
9.  L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 1: Mechanics (Nauka, Moscow, 1965; Pergamon Press, Oxford, 1976).
10.  T. G. Strizhak, Methods for Studying 'Pendulum'-Type Dynamical Systems (Nauka, Alma-Ata, 1981) [in Russian].
11.  L. D. Akulenko, "Some Rotating-Oscillating Systems Subject to High-Frequency Perturbations," Zh. Vychisl. Mat. Mat. Fiz. 8 (5), 1133-1139 (1968) [U.S.S.R. Comput. Math. Math. Phys. (Engl. Transl.) 8 (5), 272-281 (1968)].
12.  D. J. Acheson, "A Pendulum Theorem," Proc. Roy. Soc. London A 443 (1917), 239-245 (1993).
13.  V. I. Yudovich, "Vibrodynamics and Vibrogeometry of Mechanical Systems with Constraints," Uspekhi Mekh. 4 (3), 26-158 (2006).
14.  I. G. Malkin, Several Problems of Theory of Nonlinear Vibrations (Nauka, Moscow, 1956) [in Russian].
15.  O. V. Kholostova, "Stability of Periodic Motions of the Pendulum with a Horizontally Vibrating Suspension Point," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 4, 35-39 (1997) [Mech. Solids (Engl. Transl.) 32 (4), 29-33 (1997)].
16.  O. V. Kholostova, "On Motions of a Pendulum with Vibrating Suspension Point," in Theoretical Mechanics, Collection of Methodological Papers, No. 23 (Izd-vo MPI, Moscow, 2003), pp. 157-167 [in Russian].
17.  O. V. Kholostova, "On the Motions of a Double Pendulum with Vibrating Suspension Point," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 2, 25-40 (2009) [Mech. Solids (Engl. Transl.) 44 (2), 184-197 (2009)].
18.  E. A. Vishenkova and O. V. Kholostova, "To Dynamics of a Double Pendulum with a Horizontally Vibrating Point of Suspension," Vestnik Udmurt. Univ. Mat. Mekh. Komp. Nauki, No. 2, 114-129 (2012).
19.  O.V. Kholostova, "The dynamics of a Lagrange Top with a Vibrating Suspension Point," Prikl. Mat. Mekh. 63 (5), 785-796 (1999) [J. Appl. Math. Mech. (Engl. Transl.) 63 (5), 741-750 (1999)].
20.  A. P. Markeev, "On the Theory of Motion of a Rigid Body with a Vibrating Suspension," Dokl. Ross. Akad. Nauk 427 (6), 771-775 (2009) [Dokl. Phys. (Engl. Transl.) 54 (8), 392-396 (2009)].
21.  A. P. Markeev, "The Equations of the Approximate Theory of the Motion of a Rigid Body with a Vibrating Suspension Point," Prikl. Mat. Mekh. 75 (2), 193-203 (2011) [J. Appl. Math. Mech. (Engl. Transl.) 75 (2), 132-139 (2011)].
22.  A. P. Markeev, "On the Motion of a Heavy Dynamically Symmetric Rigid Body with Vibrating Suspension Point," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 4, 3-10 (2012) [Mech. Solids (Engl. Transl.) 47 (4), 373-379 (2012)].
23.  O. V. Kholostova, "On Stability of Equilibria of a Rigid Body with Vibrating Suspension Point," Vestnik RUDN. Mat. Inf. Fiz., No. 2. 111-122 (2011).
24.  O. V. Kholostova, "On Stability of Special Motions of a Heavy Rigid Body Due to Fast Vertical Vibrations of One of Its Points," Nelin. Din. 11 (1), 99-116 (2015).
Received 25 June 2015
Link to Fulltext http://link.springer.com/article/10.3103/S0025654416060029
<< Previous article | Volume 51, Issue 6 / 2016 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia (+7 495) 434-3538 mechsol@ipmnet.ru https://mtt.ipmnet.ru
Founders: Russian Academy of Sciences, Branch of Power Industry, Machine Building, Mechanics and Control Processes of RAS, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
webmaster
Rambler's Top100