Optimal design and performance evaluation of a tuned inertial damper considering soil-structure interaction effects

Abstract

The tuned inertial damper (TID) is an inerter-based damper that has been widely used to reduce the vibration of structures in seismic engineering. Due to the mass amplification effect of inertial capacity, it has become an effective substitute for conventional tuned mass damper (TMD). The design parameters in the TID are generally H₂-optimised, based on the assumption that the rigid structural foundation is excited by a stochastic white noise. However, the effect of soil-structure interaction (SSI) and the frequency dependence of the power spectral density model for stochastic ground motion are worth to be considered in the optimisation. In this regard, this paper establishes the equations of motion control for a single-degree-of-freedom (SDOF) structure equipped with a TID considering the SSI effect, and derives the mean-square value of the response of the SSI-SDOF-TID system with seismic excitation described by filtered Kanai-Tajimi (K-T) spectrum. Numerical optimisation is carried out by using a novel Nutcracker Optimisation Algorithm (NOA). The displacement, velocity and acceleration response reduction ratios of the concentrated mass supported by different soil conditions, as well as the optimal stiffness ratios and damping ratios of the corresponding TIDs, are compared to demonstrate the necessity of considering the SSI effect. Finally, the time-history responses of displacement, velocity, and acceleration of SSI-SDOF-TID system under artificial and natural seismic waves are analysed in soft soil conditions, and compared with SSI-SDOF systems. The parameter analysis shows that the optimal parameters of TID obtained for soft soil conditions with the same objectives are smaller than those of dense and medium soils, and the vibration control effect is the worst. The parameters of TID obtained from the optimisation of the same soil condition will be overestimated if the external excitation is simplified to white noise. The time-history response analysis of seismic waves in soft soil shows that the TID obtained by considering SSI has better vibration control performance.