Displacements and Forces in Structures with Inerters when Subjected to Earthquakes

Abstract

This study investigates the seismic response of a two-degrees-of-freedom structure with supplemental rotational inertia at its first story. The proposed response-modification strategy uses an inerter—a mechanical device the resisting force of which is proportional to the relative acceleration between the first story and the ground. This arrangement complements the traditional supplemental damping strategies, which are also examined in this work. The paper develops a time-domain and a frequency-domain formulation for the response analysis and shows that the seismic protection of structures with supplemental rotational inertia suppresses effectively interstory drifts at the expense of transferring appreciable forces at the support of the inerter. Both a single inerter and a pair of inerters that can only resist the motion of the structure are examined. The paper examines the extent to which a compliant support of the inerter affects the dynamics of the structure and concludes that as the compliance of the support frame increases, a single inerter may lead to a more favorable response. The proposed response-modification strategy is attractive for cases with large relative displacement demands.