Adaptive control of the rocking motion of art objects

The seismic behaviour of many art objects and obelisks can be analysed in the context of the seismic response of rigid blocks. Starting from the pioneering works by Housner (1963), a large number of analytical studies of the rigid block dynamics were proposed. In fact, despite its apparent simplicity, the motion of a rigid block involves a number of complex dynamic phenomena such as impacts, sliding, uplift and geometric nonlinearities. Methods that prevent the possible overturning were also presented in the past years, especially to protect statues and art objects with respect to seismic events. In the more general context of control, to date a current strategy is represented by base isolation. In this paper a novel adaptive control strategy for protecting monolithic art objects was investigated. The control under study follows a feedback-feedforward scheme that is realised by adjusting the stiffness of anchorages with adaptive stiffness located at the two corners of the block. A numerical comparison was made between the behaviour of the unanchored block, the anchored block with a system having constant stiffness and the anchored block with adaptive stiffness. Finally, numerical investigations were carried out in order to verify the expected efficiency of the proposed control system, and to validate simple control laws.