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Rocking bodies can be found at all structural scales, from small museum exhibits to uplifting buildings. These structures, whose dynamic stability springs from the difficulty of mobilizing their rotational inertia, are ideal candidates for benefiting from the supplemental inertia provided by inerters. This benefit can be limited, however, if the inerter drives the structural response towards potentially undesirable motions by transferring back the kinetic energy accumulated within it at inconvenient times. To control this phenomenon, a clutching system can be employed to direct the interaction between the interter and the structure improving further its dynamic behaviour. To date, however, most of the studies dealing with clutching inerto-elastic or inerto-rocking systems under seismic excitation have adopted a rather simplistic idealisation of the clutch engagement-disengagement response. In this paper, we re-visit the impact effects on inerto-rocking structures and propose an improved mechanistic model of the clutching system. First, the effects of the inerter on the transition upon impact and the impact effects on the acceleration response of rocking blocks are analysed. Then, a set of original analytical expressions for rigid and flexible rocking structures equipped with a pair of clutched inerters are derived. The newly proposed models are used to examine the evolution of the energy dissipation in the device and the influence of key parameters like the clutch stiffness, gears play, viscous damping and dry friction on its response. We conclude by evaluating the behaviour of the detailed rocking model with clutched inerters to a set of realistic earthquake ground motions. Although important differences are observed in the evolution of energy dissipation and engagement response depending on the type and characteristics of the clutch model, largely comparable peak values of displacement are obtained. On the other hand, a more accurate representation of the clutch behaviour leads to potentially larger acceleration demands. Our analyses also show that, in general, the inclusion of the inerter results in higher coefficients of restitution, indicating lower energy dissipation during impact and that the infinite acceleration spikes predicted by Housner’s model can be ignored if impact forces are sufficiently distributed over time as to cause continuous velocity transitions, but sharp enough not to appreciably affect the rotation response.

Impact and clutch nonlinearities in the seismic response of inerto-rocking systems