Seismic protection of rocking structures with inerters

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 com- parison with un-controlled 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 non-locally modifying the dynamic response of rocking structures without altering their geometry

Dynamic response of post-tensioned rocking structures with inerters

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 bene fits 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

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

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

Performance-based seismic design and assessment of rocking timber buildings equipped with inerters

Over the last decades, performance-based design objectives have shifted towards damage control and continuity of operation after a design-level earthquake. In this context, the advantages of rocking have been applied to the development of a family of self-centring systems that can sustain large lateral deformations without noticeable damage. However, the bending moments and shear forces in uplifting structures can increase significantly due to the effects of higher modes, an issue to which timber structures are particularly prone. This paper assesses the seismic response of post-tensioned timber rocking walls combined with inerters as a means to control the rotation amplitude and suppress higher-mode effects on the system. To this end, a representative set of three post-tensioned rocking walled structures, comprising 3, 6 and 9 storeys, are designed following direct-displacement based design procedures. A simplified method to pre-dimension the inerter device is proposed and used to design a set of ball screw and gear inerters, with and without clutches. The performance of bare and protected structures with different levels of apparent mass ratios is assessed and compared considering a set of 7 records consistent with the displacement design spectrum. Special attention is paid to the resisting force developed in the inerter and the mechanism to transfer it safely to the structural diaphragm. Finally, a detailed performance-based assessment is conducted considering a database of 202 pulse-like ground motion records. It is concluded that the innovative combination of inerters and rocking is an efficient way to improve the seismic control of self-centring structures

Seismic control of flexible rocking structures using inerters

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 non-coherent 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

Experimental and numerical assessment of the seismic response of steel structures with clutched inerters

Supplemental rotational inertia devices provide an efficient means of suppressing ground-induced vibrations over a large range of structural periods. The beneficial effects of the inerter can be further enhanced by coupling it with a clutch system that prevents it from driving the structural response and ensures that its supplemental rotational inertia is only employed to resist the motion. In this paper, we examine the behaviour of single-degree-of-freedom and multi-degree-of-freedom structures equipped with twin inerter- clutch devices subjected to strong ground-motion. The influence of the clutch stiffness, gears play, viscous damping and dry friction, on the dynamics of the system are explored first, by analysing the stable periodic solutions of a structure with inerters under harmonic-sweeps. We demonstrate that, for the range of param- eters typically expected in earthquake engineering practice, the influence of dry-friction and clutch damping are limited, although the clutch stiffness and gear play may need to be accounted for when large inertances or defective clutches are considered. Based on these findings, we propose a simplified numerical modelling strategy suitable for implementation in conventional Finite Element simulations. Small scale experiments on bare elastic structures as well as structures equipped with inerter and inerter-clutch twins are presented and employed for concept demonstration and for the validation of the numerical model proposed. Finally, a series of studies on detailed numerical models of multi-storey steel frames under idealized and real pulse-like ground-motions are used to demonstrate the vibration absorbing capabilities brought about by the twin inerter-clutch system and to highlight practical aspects related to their structural implementation