This article is cited in 4 papers

Nonlinear Systems

Dynamics of a parallelepiped on a horizontal vibrating plane

A. V. Karapetyan^a, M. A. Munitsyna<sup>b

a</sup> Moscow State University, Moscow, Russia
^b Moscow Institute of Physics and Technology (State University), Dolgoprudny, Russia

Abstract: We consider the dynamics of a rigid parallelepiped on a horizontally vibrating rigid support plane and the possibility to control its oscillations. We assume that there is no slipping of the parallelepiped's base along the plane. We find such excitation parameters for which the parallelepiped breaks off from the plane and performs oscillations, resting upon alternating support edges. In case of harmonic oscillations of the plane, we find possible modes of forced oscillations. We study the problem of reducing the amplitude of oscillations for the parallelepiped with a mathematical pendulum. We show results as frequency and phase responses.

Presented by the member of Editorial Board: V. N. Tkhai

Received: 14.11.2013

 English version: Automation and Remote Control, 2015, 76:3, 394–404

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