Enhancing the seismic resilience of structures by using optimum combination of tuned mass damper inerter and negative stiffness damper

This paper presents a study on optimizing the combination of a tuned mass damper inerter and a negative stiffness damper (TMDI-NSD) for better performance of structures against seismic actions. The experimental data obtained from the literature were used in the optimization of a hybrid combination of TMDI-NSD subjected to harmonic excitation considering different stability maximization criteria (SMC). The H2 optimization technique was used to obtain the optimum tunning parameter using the numerical method, while the closed form of the optimum technique was used to obtain the optimum tunning parameter through the SMC optimization technique. The maximum dynamic amplification factor (DAFmax) was considered for a comparison of TMDI-NSD. The results show that the performance of a TMDI-NSD combination is superior compared to that of a TMD. In addition, it is found that the performance of SMC is less compared to H2 & H∞ criteria, but the performance of H2 & H∞ is equivalent. The DAFmax value increases with the increase in the mass ratio for the TMDI-NSD combination, whereas it declines with the rise in the mass ratio for TMD. Besides, the performance of the damped primary system under seismic load with and without the TMDI-NSD combination was analyzed. Twenty real earthquake ground motion data were considered in the analysis. The response of the primary system mitigated with the TMD and TMDI-NSD combination was evaluated in terms of the broad frequency range efficiency and peak value. It is observed that the damped primary system with TMDI-NSD combination using under-optimization criteria is superior to TMDI-NSD with respect to the displacement response. However, when considering the acceleration response, the SMC performs better compared to H2 & H∞ optimization criteria. The acceleration and displacement response for the primary structural system is reduced by 60% and 75%, respectively, by using TMDI-NSD of SMC optimization. Finally, the investigation of the single primary degree of freedom for a system with a TMDI-NSD combination indicates that all three optimization criteria under real seismic excitation perform better.