The nonlinear dynamic analysis of optimum nonlinear inertial amplifier base isolators for vibration isolation

The nonlinear inertial amplifier base isolators (NIABI) for dynamic response mitigation of structures are introduced in this paper. The nonlinear inertial amplifiers are installed inside the core of the traditional base isolators (TBI) to upgrade their vibration reduction capacity. The equivalent linearization method applies to linearize each element from highly nonlinear equations of motion of nonlinear NIABI to derive the optimal closed-form solutions for nonlinear NIABI. Therefore, H-2 and H-infinity optimization methods are applied to derive the exact closedform expressions for optimal design parameters of NIABI, linearized NIABI, and TBI analytically. Initially, the dynamic responses of the structures isolated by the NIABI, linearized NIABI, and TBI are obtained through the transfer function formation. Thus, the dynamic response reduction capacities of H2 and H-infinity optimized NIABI are significantly 38.55% and 65.14% superior to the H-2 and H-infinity optimized TBI. In addition, the nonlinear dynamic responses of the isolated structures are also derived analytically through the harmonic balancing method. Therefore, the dynamic response reduction capacities of H-2 and H-8 optimized nonlinear NIABI are significantly 44.51%, 39.80%, 35.81% and 90.10%, 77.49%, 67.66% superior to the H-2 and H-infinity optimized TBI, inertial amplifier base isolator (IABI), linearized version of nonlinear inertial amplifier base isolator (linearized NIABI). The effectiveness of the optimum NIABI has been studied further by a numerical study using the Newmarkbeta method with near-field earthquake base excitations (pulse records). Accordingly, the displacement and acceleration response reduction capacities of the optimum NIABI are 14.47% and 22.23% superior to the optimum TBI. The overall result shows that the non-linearity of the inertial amplifiers increases the dynamic response reduction capacity of the traditional base isolators and inertial amplifier base isolators. All of the results are mathematically accurate and suitable for practical applications.