Effectiveness of mass–damper dynamic absorber on rocking block under one-sine pulse ground motion

In this paper the effects of a mass–damper on the rocking motion of a rigid block, subject to one-sine pulse-type excitation, is investigated. The damper is modelled as a single-degree-of-freedom oscillating mass, running at the top of the block and connected to it by a linear visco-elastic device. In a previous paper by the same authors the effectiveness of the oscillating mass–damper was investigated on a block with fixed dimensions, by performing a parametric analysis where only the characteristics of the damper were changed. Instead, in this paper the variable parameters are those characterizing the block that has to be protected. The equations of rocking motion and the uplift and impact conditions are derived by means of a direct approach, capable of providing a deeper interpretation of the forces acting on the system. An extensive parametric analysis is performed by numerical integration of the governing equations and by taking the dimensions of the block, the frequency and the amplitude of the excitation, and the period of the oscillating mass as variable parameters. Curves capable of providing the amplitude of the excitation for which an overturning of the block occurs are obtained and the role of the variable parameters is pointed out. Finally, curves providing the threshold frequency of the one-sine excitation above which the mass–damper does not work well are obtained, depending on the parameters characterizing the block.