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IssuesArchive of Issues2011-4pp.495-507

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Total articles in the database: 10864
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V.Ph. Zhuravlev and G.M. Rozenblat, "On the Instability of a Car in the Vertical Plane under Rectilinear Motion with Friction Forces Taken into Account," Mech. Solids. 46 (4), 495-507 (2011)
Year 2011 Volume 46 Number 4 Pages 495-507
DOI 10.3103/S0025654411040017
Title On the Instability of a Car in the Vertical Plane under Rectilinear Motion with Friction Forces Taken into Account
Author(s) V.Ph. Zhuravlev (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str.1, Moscow, 119526 Russia, zurav@ipmnet.ru)
G.M. Rozenblat (Moscow State Automobile and Road Technical University, Leningradskii pr-t 64, Moscow, 125319 Russia, gr51@mail.ru)
Abstract We consider the problem on the stability and instability of the equilibrium in the vertical plane for a wheeled vehicle performing a uniform rectilinear motion in the presence of rolling friction forces. We assume that the dependence of the rolling friction coefficients on the motion velocity is known and derive necessary and sufficient conditions on the system parameters under which such equilibria are stable.
Keywords wheeled vehicle, equilibrium stability, rolling friction, dissipation
References
1.  A. Yu. Ishlinskii, "On the Rolling Friction," Prikl. Mat. Mekh., No. 2, 245-260 (1939) [J. Appl. Math. Mech. (Engl. Transl.)] (See also A. Yu. Ishlinskii, "On the Rolling friction," in Applied Problems of Mechanics, Book 1: Mechanics of Viscoplastic and Not-Completely-Elastic Bodies (Nauka, Moscow, 1986), pp. 176-190 [in Russian]).
2.  M. A. Levin and N. A. Fufaev, Theory of Rolling of a Deformable Wheel (Nauka, Moscow, 1989) [in Russian].
3.  State Standard (GOST) R 52102-2003. Pneumatic Tires. Determination of the Rolling Resistance by the Retardation Method (State Standard of Russian Federation, Moscow, 2003) [in Russian].
4.  A. A. Khachaturov, V. L. Afanas'ev, V. S. Vasil'ev, and G. V. Gol'din, The Dynamic Road-Tire-Vehicle-Driver System, Ed. by A. A. Khachaturov (Mashinostroenie, Moscow, 1976) [in Russian].
5.  V. P. Tarasik, Theory of Car Motion: Manual for Higher Educational Institutions (BKhV-Peterburg, St. Petersburg, 2006) [in Russian].
6.  K. Magnus, Kreisel. Theorie und Anwendungen (Springer, Berlin, 1971; Mir, Moscow, 1974).
7.  V. Ph. Zhuravlev, "Decomposition of Nonlinear Generalized Forces into Potential and Circulatory Components," Dokl. Ross. Akad. Nauk 414 (5), 622-624 (2007) [Dokl. Phys. (Engl. Transl.) 52 (6), 339-341 (2007)].
8.  D. R. Merkin, Introduction to Theory of Stability of Motion (Nauka, Moscow, 1971) [in Russian].
9.  I. Rokar, Instability in Mechanics. Automobiles. Airplanes. Suspension Bridges (Izd-vo Inostr. Lit., Moscow, 1959) [in Russian].
10.  V. Ph. Zhuravlev, Foundations of Theoretical Mechanics (Fizmatlit, Moscow, 2008) [in Russian].
11.  V. Ph. Zhuravlev and G. M. Rozenblat, "On Vibrations of a Wheel Carriage in the Presence of Friction Academician," Dokl. Ross. Akad. Nauk 436 (5), 1-4 (2011) [Dokl. Phys. (Engl. Transl.) 56 (2), 118-121 (2011)].
12.  V. Ph. Zhuravlev and D. M. Klimov, Applied Methods in Vibration Theory (Nauka, Moscow, 1988) [in Russian].
Received 11 January 2011
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