Original papers

Oscillations of a solid parallelepiped on a supported base

A. I. Munitsyn^a, M. A. Munitsyna<sup>b

a</sup> National Research University “Moscow Power Engineering Institute”, Krasnokazarmennaia 14, Moscow, Russia, 111116
^b Moscow Institute of Physics and Technology, 9 Institutskiy per., Dolgoprudny, Moscow Region, 141700, Russian Federation

Abstract: An analytical solution of the problem of forced oscillation of the solid parallelepiped on a horizontal base is presented. It is assumed that the slippage between the body and the base is absent, and the base moves harmonically in a horizontal direction. It is also assumed that the height of the box is much larger than the width. The dissipation of impact is taken into account in the framework of Newton’s hypothesis. The forced oscillation modes of parallelepiped corresponding to the main and two subharmonic resonances are found by using the averaging method. The results are shown in the form of amplitude-frequency characteristics.

Keywords: supported plane, nonlinear oscillations, averaging method.

UDC: 531.46

MSC: 70F40

Received: 10.12.2015
Revised: 22.02.2016