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IssuesArchive of Issues2017-6pp.675-685

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A.I. Munitsyn, "Vibrations of a Rigid Body with Cylindrical Surface on a Vibrating Foundation," Mech. Solids. 52 (6), 675-685 (2017)
Year 2017 Volume 52 Number 6 Pages 675-685
DOI 10.3103/S0025654417060073
Title Vibrations of a Rigid Body with Cylindrical Surface on a Vibrating Foundation
Author(s) A.I. Munitsyn (National Research University "Moscow Power Engineering Institute," ul. Krasnokazarmennaya 14, Moscow, 111250 Russia, munitsyn@rambler.ru)
Abstract The analytic solution of the problem of forced vibrations of a rigid body with cylindrical surface on a horizontal foundation is given. It is assumed that the dry friction force acts at the point of contact between the cylindrical surface of the body and the foundation and the foundation moves by a harmonic law in the horizontal direction perpendicularly to the cylindrical surface element. The averaging method is used to determine the forced vibration mode near the natural frequency of the body vibrations on the fixed foundation. The results are presented as amplitude-frequency and phase-frequency characteristics.
Keywords supporting plane, dry friction, nonlinear oscillations, averaging method
References
1.  A. P. Markeev, Dynamics of a Body Contacting with a Rigid Surface (Moscow-Izhevsk, Inst. Komput. Issled., 2014) [in Russian].
2.  I. I. Blekhman and G. Yu. Dzhanilidze, Vibrational Motion (Moscow, Nauka, 1964) [in Russian].
3.  R. F. Nagaev, Periodic Regimes of Vibrational Motion (Moscow, Nauka, 1978) [in Russian].
4.  S. J. Hogan, "The Many Steady State Responses of a Rigid Block under harmonic Forcing," Earthquake Engng Struct. Dyn. 19, 1057-1071 (1990).
5.  U. Andreaus and P. Casini, "On the Rocking-Uplifting Motion of a Rigid Block in Free and Forced Motion: Influence of Sliding and Bouncing," Acta Mech. 138, 219-241 (1999).
6.  A. Sinopoli, "Unilaterality and Dry Friction: A Geometric Foundation for Two-Dimensional Rigid Body Dynamics," Nonlin. Dyn. 12 (4), 343-366 (1997).
7.  V. V. Andronov and V. Ph. Zhuravlev, Dry Friction in Problems of Mechanics (NITs "Regular and Chaotic Dynamics," Moscow-Izhevsk, 2010) [in Russian].
Received 05 April 2016
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