The nonlinear negative stiffness inertial amplifier base isolators for dynamic systems

The nonlinear negative stiffness inertial amplifier base isolators (NNSIABI) for vibration reduction of dynamic systems are introduced in this paper. H-2 and H-infinity optimization methods are applied to derive the exact closed-form expressions for the optimal design parameters of novel isolators. For SDOF system, the dynamic response reduction capacity of H-2 and H-infinity optimized linear NSIABI are significantly 64.78% and 77.14% superior to the optimum traditional base isolators. In contrast, the dynamic response reduction capacities of H-2 and H-infinity-optimized nonlinear NNSIABI are significantly 64.66% and 66.56% superior to the optimum traditional base isolators. For MDOF systems, the optimum linear NSIABI's dynamic response reduction capacities are significantly 95.06% and 97.80%, superior to the optimum traditional base isolators. In addition, the optimum nonlinear NNSIABI are significantly 94.88% and 97.68%, superior to the traditional base isolators. All the results are mathematically corrected and applicable for practical applications.