Dynamics of an Inhomogeneous Ball on a Vibrating Base with Two-Component Viscous Friction

Abstract

The problem of forced oscillations of a heavy inhomogeneous ball placed on a horizontal base is considered. It is assumed that the base moves in a horizontal direction according to harmonic law and at the point of contact between the surface of body and the base, the force and moment of viscous friction act. The equations of motion for a mechanical system are derived. Their solution is obtained by the averaging method. The dependences of the oscillation amplitudes for the excitation frequencies close to the eigenfrequency of the oscillations of the inhomogeneous ball on an absolutely smooth base are constructed. Both plane and spatial modes of oscillations have been found.