Dynamic behaviour of two stacked rigid blocks

The study of the rocking response of statues and in general the objects contained within Museums, is a research topic of great interest, being part of research and policy in the more general field of Cultural Heritage. The seismic protection of buildings of historical and cultural significance has been developed in all the last century. The protection of the contained objects, with reference to how they are displayed or stored, has become only in the last years a key question. Significant is the case of statues and ceramics placed on pedestals. In particular cases, like the Bronzes of Riace, on purpose isolation systems have been developed, while in general museum exhibitions are not equipped with devices capable of mitigating the oscillations induced by possible earthquakes. This paper focuses the attention on this last problem, i.e. objects that can be considered as rigid bodies simply supported on the main structure. This problem is the same of a large class of non-structural components, such as mechanical and electrical hospital and laboratory equipments that can lose their functionality because of earthquake motions. This paper presents the theoretical and numerical bases of a simple and low cost isolation system to protect small art objects, as the first step toward the choice of the optimal friction coefficient to be created in the pedestal. In fact the insertion of a further rigid body between the moving base and the statue can reduce the effect of base motion due to earthquakes. The results of an analysis made by means of a numerical procedure on purpose developed are presented The problem studied concerns the motion of two superimposed blocks of different aspect ratio: a top slender block placed on a flat one, both on a moving base. The hypotheses are made in order to represent the real situation of a marble statue placed on a flat rigid pedestal freestanding on a moving floor.