Free Damped Vibrations of Rocking Rigid Blocks as Uniformly Accelerated Motions

This paper introduces a novel formulation for the free rocking motion of a rigid block supported on a rigid plane. The equation of the motion between two subsequent impacts is expressed as a uniformly accelerated motion only depending on the assigned initial velocity. The constant acceleration is derived by an ad hoc approximation in order to fit the results of the standard model of Housner (1963), which is herein revisited and explored. An extensive comparison between the standard and the proposed models is carried out in terms of moment-rotation relationship, critical rotational velocity, normalized amplitude and duration of the half-cycles.