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 Nelin. Dinam., 2018, Volume 14, Number 4, Pages 519–542 (Mi nd629)

Nonlinear physics and mechanics

On the Motion of a Body with a Moving Internal Mass on a Rough Horizontal Plane

Bardin B. S.ab, Panev A. S.a

a Moscow Aviation Institute (National Research University), Volokolamskoe sh. 4, Moscow, 125993 Russia
b Mechanical Engineering Research Institute of the Russian Academy of Sciences (IMASH RAN), M. Kharitonyevskiy per. 4, Moscow, 101990 Russia

Abstract: We consider a vibration-driven system which consists of a rigid body and an internal mass. The internal mass is a particle moving in a circle inside the body. The center of the circle is located at the mass center of the body and the absolute value of particle velocity is a constant. The body performs rectilinear motion on a horizontal plane, whereas the particle moves in a vertical plane. We suppose that dry friction acts between the plane and the body. We have investigated the dynamics of the above system in detail and given a full description of the body’s motion for any values of its initial velocity. In particular, it is shown that there always exists a periodic mode of motion. Depending on parameter values, one of three types of this periodic mode takes place. At any initial velocity the body either enters a periodic mode during a finite time interval or it asymptotically approaches the periodic mode.

Keywords: periodic motion, dry friction, rigid body, vibration-driven system

 Funding Agency Grant Number Russian Science Foundation 14-21-00068 This research was supported by a grant of the Russian Science Foundation (project No 14-21-00068).

DOI: https://doi.org/10.20537/nd180407

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MSC: 70E18
Accepted:15.09.2018
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Citation: Bardin B. S., Panev A. S., “On the Motion of a Body with a Moving Internal Mass on a Rough Horizontal Plane”, Nelin. Dinam., 14:4 (2018), 519–542

Citation in format AMSBIB
\Bibitem{BarPan18} \by Bardin B. S., Panev A. S. \paper On the Motion of a Body with a Moving Internal Mass on a Rough Horizontal Plane \jour Nelin. Dinam. \yr 2018 \vol 14 \issue 4 \pages 519--542 \mathnet{http://mi.mathnet.ru/nd629} \crossref{https://doi.org/10.20537/nd180407} \elib{https://elibrary.ru/item.asp?id=36686072}