This article is cited in 4 papers

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.<sup>a

a</sup> 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.

MSC: 70E18

Received: 16.08.2018
Accepted: 15.09.2018

Language: English

DOI: 10.20537/nd180407

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