Rocking resonance of a rigid free standing block

This paper deals with the resonance conditions of a rigid free standing block in order to highlight to what extent the ground motion details and the system parameters can influence the rocking response. A sequence of instantaneous pulses causing "rocking resonance" is first explored and the natural motion occurring between two impacts is then investigated. The coefficient of restitution is assumed to be a variable of the problem to account also for other damping effects (e.g. local plastic deformations). A stabilized phase of the motion is identified for which an upper-bound of the maximum rotation angle of the block can be defined in closed form. The results are plotted in resonance spectra which point out the influence of the coefficient of restitution and the size and slenderness of the block.