Robust control design of nonlinear negative stiffness base isolators for MDOF systems

Seismic isolation is crucial for protecting structures from earthquake-induced vibrations, yet traditional base isolators (TBI) often exhibit limitations in mitigating dynamic responses, particularly in multi-degree-of-freedom (MDOF) systems. This study introduces nonlinear negative stiffness base isolators (NNBI) as an advanced alternative, leveraging H 2 optimisation to enhance vibration control. A mathematical framework was developed to derive closed-form expressions for optimal NNBI design parameters, followed by numerical validation through frequency and time-domain analyses, including harmonic excitations, random white noise, and near-field earthquake simulations. Results demonstrated that NNBI achieves at least 47.90 % greater dynamic response reduction compared to TBI, with a maximum improvement of 97.80 % for ten DOF systems, confirming its superior energy dissipation capabilities. These findings establish NNBI as a transformative solution for seismic resilience, with potential applications in tall buildings. • Nonlinear negative stiffness base isolators for MDOF systems are introduced. • H 2 optimised design parameters are introduced. • NNBI’s vibration reduction capacity is 92.9 % greater than TBI’s. • NNBI’s vibration reduction capacity is 96.58 % more than TBI for ten DOF. • NNBI is more effective for higher degrees of freedom systems than TBI.