Oscillations of rigid block on supported base with coulomb friction model

Abstract

The analytical solution of the problem of forced oscillation of the solid parallelepiped on a horizontal base is presented. It is assumed that the dry friction force acts on the contact line between the body and the base and the base moves harmonically in a horizontal direction. The height of the parallelepiped is assumed to be much greater than the width. Dissipation of impact is taken into account in the framework of the hypothesis of Newton. The forced oscillation modes of parallelepiped corresponding to the main resonances are found by using the averaging method. The results are shown in the form of amplitude-frequency characteristics.

Dynamic of a cylindrical column on a vibrating base

“…There are other technical areas of application of this problem, for example, the problem of the movement of parts on a conveyor. The exact solution to the problem of vibrations of a parallelepiped on a vibrating base was obtained in [5], and in [6,7] the averaging method was used, which made it possible to investigate the stability of the solutions obtained. A detailed list of publications on the issue of seismic stability of elongated structures is given in [8].…”