3D model of rigid block with a rectangular base subject to pulse-type excitation

A model of 3D rigid body with a rectangular base, able to rock around a side or a vertex of the base is developed. Eccentricity of the center of mass with respect to the geometrical center of the body is also considered. The equations of motion are obtained through the general balance principle. A one-sine pulse base excitation is applied to the body in different directions. The analyses are conducted with the aim to highlight the role of the period, the amplitude and the direction of the external excitation. In significant ranges of the previous parameters, the results obtained with a bi-dimensional model, that does not consider the 3D rocking motions on a vertex of the base, are not in favor of safety. It is found, in fact, that in several conditions the overturning of the 3D block takes place for amplitudes of excitation smaller than those able to overturn the 3D block.