Optimal design of negative-stiffness dampers for improved efficiency of structural seismic isolation

Over the past two decades, negative-stiffness devices have attracted increasing interest in the community of structural vibration isolation and control. They are typically used in combination with supplemental damping devices, and the combined systems are often referred to as negative-stiffness dampers (NSDs). Different types of NSDs have been developed and studied using both theoretical and experimental methods. However, comprehensive comparative studies between optimally designed NSDs for improving the efficiency of structural seismic isolation are inadequate. In this paper, three types of NSDs, i.e., the negative-stiffness viscous damper (NSVD), negative-stiffness viscoelastic damper (NSVeD), and negative-stiffness inertoviscous damper (NSiVD) are considered and compared in terms of their efficiencies for structural seismic isolation. Analytical formulas are derived to calculate the optimal damping coefficients of the NSVeD and NSiVD to maximize the modal damping ratio, thus minimizing the peak transmissibility. Frequency- and time-domain responses of low-frequency structures separately equipped with the three types of NSDs are compared when they are designed to achieve equal modal damping ratios. Moreover, based on the derived analytical optimal formulas, a multi-objective minimization design method is presented to determine the optimal characteristic parameters of NSDs, and simultaneous reduction of isolator displacement and floor response acceleration of a benchmark base-isolated building structures under a suit of design-level ground motions is achieved. The results indicate that the three types of NSDs can be more effective than conventional viscous dampers in reducing floor response accelerations of base-isolated structures without compromising the isolator displacement, and the NSVeD has superior performance over the NSVD and NSiVD in terms of improved efficiency of structural seismic isolation.