Summary The seismic behaviour of a wide variety of structures can be characterized by the rocking response of rigid blocks. Nevertheless, suitable seismic control strategies are presently limited and consist mostly on preventing rocking motion all together, which may induce undesirable stress concentrations and lead to impractical interventions. In this paper, we investigate the potential advantages of using supplemental rotational inertia to mitigate the effects of earthquakes on rocking structures. The newly proposed strategy employs inerters, which are mechanical devices that develop resisting forces proportional to the relative acceleration between their terminals and can be combined with a clutch to ensure their rotational inertia is only employed to oppose the motion. We demonstrate that the inclusion of the inerter effectively reduces the frequency parameter of the block, resulting in lower rotation seismic demands and enhanced stability due to the well‐known size effects of the rocking behaviour. The effects of the inerter and inerter‐clutch devices on the response scaling and similarity are also studied. An examination of their overturning fragility functions reveals that inerter‐equipped structures experience reduced probabilities of overturning in comparison with uncontrolled bodies, while the addition of a clutch further improves their seismic stability. The concept advanced in this paper is particularly attractive for the protection of rocking bodies as it opens the possibility of nonlocally modifying the dynamic response of rocking structures without altering their geometry.

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Allowing flexible structures to uplift and rock during earthquakes can significantly reduce the force demands and residual displacements. However, such structures are still susceptible to large deformations and accelerations that can compromise their functionality. In this paper, we examine the dynamic response of elastic rocking oscillators and suggest that their lateral drifts and accelerations can be limited effectively by using inerter devices. To this end, we offer a detailed examination of the effects of structural flexibility on the efficiency of the proposed system. The analytical expressions governing the motion of deformable structures with base uplift are revisited to incorporate the effects of the supplemental rotational inertia. The proposed model is then used to study the structural demands of flexible rocking structures under coherent pulses as well as noncoherent real pulse-like ground motions. Our results show that combining rocking with inerters can be an efficient strategy to control the deformation and acceleration demands in uplifting flexible systems.

Post-tensioned rocking systems have proved to be highly effective in controlling structural damage during strong ground motions. However, recent events have highlighted the importance of looking at both the structural and non-structural components within a holistic framework. In this context, the high rotations and accelerations associated with the rocking motion can cause significant non-structural damage and affect the performance and functionality of the entire system. In this paper, we examine analytically the fundamental dynamics of post-tensioned rocking structures and investigate the benefits of using supplemental rotational inertia to reduce their seismic demands and improve their overall performance. The newly proposed strategy employs inerters, a mechanical device that develops a resisting force proportional to the relative acceleration between its terminals. Analyses conducted for a wide range of acceleration pulses and real pulse-like ground motions show that post-tensioned structures equipped with inerters consistently experience lower demands and have reduced probabilities of exceeding limit states typically associated with damage. Importantly, the new vibration control strategy advanced in this paper opens the door for an expedient modification of the fundamental dynamic response of rocking systems without altering their geometry.

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