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

Abstract

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 *Manuscript Click here to download Manuscript: Manuscript.docx Click here to view linked References

Seismic protection of rocking structures with inerters

“…In comparison with studies concerning the estimation of rocking response, investigations on control strategies suitable to rocking bodies have been more limited and have mainly concentrated on the protection of museum artefacts and nonstructural equipment. 25,26 Early strategies were based on simple measures, such as lowering the centre of mass or anchoring the object to a fixed support. 27,28 While the former approach is not very practical, the latter prevents the rigid-body rocking motion and may therefore induce undesirable deformations that can damage the object.…”

Rocking and Kinematic Approaches for Rigid Block Analysis of Masonry Walls: State of the Art and Recent Developments

“…Makris et al [78] introduced a useful representation in terms of overturning spectra of blocks, which describe the stability of a given block in terms of the maximum acceleration amplitude as a function of the block size or the excitation frequency (Section 7.2). These kinds of spectra can also be developed to perform interesting strategies for the seismic protection of monolithic art objects, as the semi-active control proposed by Ceravolo et al [79,80] or the addition of a tuned pendulum to the rocking block with the aim of controlling the oscillations presented by Collini et al [81]. This deterministic method is affected by some limitations, mainly related to the need for using significant acceleration time-histories.…”

Semiactive control of rigid blocks under earthquake excitation

“…In the present work, the control law used to set the stiffness K ( t ) of the anchorages during the rocking motion is that proposed by Ceravolo et al The main characteristic of this control law is that it preserves the positive effect on the body stability of the anchorage with constant stiffness and minimizes/overcomes the negative one. Indeed, studying the stability of bodies anchored with elastic‐brittle anchorages, Makris et al and Dimitrakopoulos et al found that the presence of anchorages increases the minimum acceleration required for the body to overturn, but it also boosts its tendency to overturn after the impact.…”

“…A couple of strategies different from the base isolation were recently proposed that reduce the overturning vulnerability while allowing the object to rock. More specifically, De Leo et al proposed a passive tuned mass damper hinged at the top of the block, while Ceravolo et al proposed a semiactive control.…”

“…[23][24][25][26] A couple of strategies different from the base isolation were recently proposed that reduce the overturning vulnerability while allowing the object to rock. More specifically, De Leo et al 27 proposed a passive tuned mass damper hinged at the top of the block, while Ceravolo et al [28][29][30] proposed a semiactive control. This paper examines the usefulness of the semiactive control to reduce the overturning vulnerability of a rigid block on a rigid plane.…”