Optimal design and seismic performance of tuned mass damper inerter (TMDI) for structures with nonlinear base isolation systems

The tuned mass damper inerter (TMDI) couples the classical tuned mass damper (TMD) with an inerter, a mechanical device whose generated force is proportional to the relative acceleration between its terminals, thus providing beneficial mass-amplification effects. This paper deals with a dynamic layout in which the TMDI is installed below the isolation floor of base-isolated structures in order to enhance the earthquake resilience and reduce the displacement demand. Unlike most of the literature studies that assumed a linearized behavior of the isolators, the aim of this paper is to investigate the effectiveness of the TMDI while accounting for the nonlinearity of the isolators. Two nonlinear constitutive behaviors are considered, a Coulomb friction model and a Bouc-Wen hysteretic model, representative of friction pendulum and of lead-rubber-bearing isolators, respectively. Optimal design is based on the stochastic dynamic analysis of the system, by modeling the base acceleration as a Kanai-Tajimi filtered stationary random process and resorting to the stochastic linearization technique to handle the nonlinear terms. Different tuning criteria based on displacement, acceleration, and energy-based performance indices are defined, and their implications in a design process are discussed. It is proven that the improved robustness of the TMDI reduces its performance sensitivity to the tuning frequency and to the earthquake frequency content, which are well-known shortcomings of TMD-like systems. This important feature makes the TMDI particularly suitable for nonlinear base-isolated structures that are affected by unavoidable uncertainties in the isolators' properties and that may experience changes of isolators effective stiffness depending on the excitation level.