On rocking of a rigid body on a moving rough plane

One of the most destructive effects of earthquakes upon buildings and other constructions is due to horizontal displacement of the ground. This paper proposes a simplified approach to description of behavior of tower-like structures in such conditions. For this aim, a plane-parallel motion of a rigid body over horizontal plane with dry friction is considered. It is assumed that the plane performs harmonic oscillations in horizontal direction. In order to describe collisions between the body and the supporting plane, Routh hypothesis is used. Conditions of overturning of the body are obtained for different values of amplitude and frequency of oscillations of the plane, depending on model parameters, such as body aspect ratio, friction coefficient, coefficient of restitution, etc.