Multi-modal Multi-response Seismic Mitigation with Amplified Inerter Negative Stiffness Dampers

This study develops an innovative seismic control system that integrates Scissor-jack Toggle-brace amplification mechanisms with Tuned Inerter Negative Stiffness Dampers (TINSDs) to address unresolved challenges in multi-modal multi-response targeted vibration mitigation. First, a novel equivalent amplification factor was proposed to provide a unified metric considering both device amplification and inter-story installation effects, enabling efficient reduced-order modeling and optimal design. Second, closed-form H∞/H2 solutions were rigorously derived, which reveals inherent Pareto-optimal performance trade-offs across displacement, acceleration, and force transmissibility response targets. Third, a novel method integrating Master Oscillator Principle (MOP) and Pareto optimization was proposed. By decomposing the complex problem into optimally allocated damper groups, simultaneous control of fundamental-mode displacements and higher-mode accelerations/reaction forces was achieved. Benchmark validation studies demonstrate remarkable performance improvements compared to conventional single-modal approaches. The proposed system achieves significant reductions in total required inertance and damping coefficients while maintaining comparable displacement control effectiveness and significantly enhancing acceleration and reaction force mitigation. Furthermore, a practical rule-of-thumb allocation strategy featuring progressive base-to-top targeting of lower-to-higher modes with decreasing device density was developed, which shows statistically equivalent performance Pareto-optimized solutions (p>0.05). The proposed framework offers both sophisticated control algorithms for researchers and implementable guidelines for engineers.