Semi-active control of the rocking motion of monolithic art objects

• A new semi-active strategy to control rocking motion in rigid bodies is proposed.
• Overturning spectra diagrams are calculated and presented for controlled blocks.
• The control strategy is applied to a model of the S. Matteo statue by Michelangelo.

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, 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. While most of the current strategies to avoid toppling consist in preventing rocking motion, in this paper a novel semi-active on–off control strategy for protecting monolithic art objects was investigated. The control procedure under study follows a feedback–feedforward scheme that is realised by switching the stiffness of the anchorages located at the two lower corner of the block between two values. Overturning spectra have been calculated in order to clarify the benefits of applying a semi-active control instead of a passive control strategy. In accordance with similar studies, the numerical investigation took into account the dynamic response of blocks with different slenderness and size subject to one-sine pulse excitation.