On the rocking-uplifting motion of a rigid block in free and forced motion: influence of sliding and bouncing.

The problem of rocking response of a rigid block in free and forced motion has been studied for a number of technical reasons. Apart from the technical interests, the problem of rigid block rocking is intrinsically of interest from a theoretical point of view. In fact, the problem is highly nonlinear in nature. Aim of this paper is to study the contact-impact problem of a rigid block colliding on a frictional base, by means of a numerical simulation, and to compare numerical results with analytical responses known from the literature. The influence of sliding and bouncing on the orbit type and stability is analyzed by a 3-DOF model of the system and by a new refined model of the contact forces between block and base. Furthermore, attention has been paid to two-dimensional free motion of the block with three degrees of freedom. Refined analytical stress-strain relations in either normal and tangential directions with respect to the contact surfaces are formulated which allow to account for (i) up-lifting and hysteretic damping in normal direction, (ii) coupling between shear strength and compression force, friction dissipation and cumulating damage in tangential direction.