The optimal configuration of negative stiffness inerter-based base isolators in multi-storey buildings

Abstract

The negative stiffness inerter-based base isolators (NSIBI) are introduced in this paper. The negative stiffness device and inerters are installed inside the core of the conventional base isolators (CBI) to enhance their dynamic response reduction capacity. The novel isolators have been installed at the multi-storey building’s base to mitigate their dynamic responses during vibration. H2 optimization method applies to derive the exact closed-form expression for negative stiffness inerter-based base isolators’ optimal design parameters, such as frequency and viscous damping ratio for multi-storey buildings. Applying these H2 optimized design parameters, the optimum NSIBI for dynamic response mitigation of multi-storey buildings have been achieved. The dynamic responses of the NSIBI-controlled multi-storey buildings are compared with the dynamic responses of multi-storey buildings isolated by optimum CBI to determine the exact superior dynamic response reduction capacity of optimum NSIBI. The dynamic responses of isolated structures in the frequency domain are evaluated by forming the transfer function. Therefore, for five-storey buildings, the dynamic response reduction capacity of NSIBI is significantly 51.93% and 81.24% superior to the dynamic response reduction capacity of CBI subjected to harmonic and random-white excitations. In contrast, for ten-storey buildings, the optimum NSIBI has 77.73% and 94.02% more dynamic response reduction capacity than the optimum CBI subjected to harmonic and random-white excitations. In addition, using the Newmark beta method, a numerical study further conducts to verify the accuracy of the H2 optimized design parameters by obtaining the time history results for isolated structures subjected to near-field pulse-type earthquake base excitations. Accordingly, the optimum NSIBI have 57.591% and 55.398% more displacement and acceleration capacity than the optimum CBI for five-storey buildings. Besides, for ten-storey buildings, the displacement and acceleration capacities of optimum NSIBI are significantly around 56.42%and 55.80%, superior to the optimum CBI. Thus, the vibration reduction capacity of optimum CBI is significantly decreasing while the storey level of the multi-storey buildings increases, whereas NSIBI is still efficient in reducing the dynamic responses effectively. The paper’s outcomes are mathematically accurate and applicable to practical implementation.