Performance Evaluation and Comparative Analyses of Tuned Inerter Damper for Stochastic Base Excited Structures Based on Hybrid H2/H∞ Optimization

Compared with tuned mass damper, tuned inerter damper (TID) has higher damping efficiency and lightweight characteristic if appropriate optimal methods are selected. Generally, H-infinity or H-2 optimal methods are adopted to determine the optimal parameters of TID individually. But the vibration mitigation performance of the TID under near resonance frequency band based on H-infinity optimization is less than H-2 optimization, but the peak frequency response based on H-2 optimization will be greater than H infinity optimization at the same time. Dual-characteristic-based vibration control may not be achievable based on H-infinity or H-2 criteria, respectively. For this reason, hybrid H-2/H-infinity optimization can be adopted. In this work, closed-form expressions are derived for the control of structural displacement responses based on hybrid H-2/H-infinity optimal method. The vibration mitigation performance of the different optimized TIDs is evaluated considering the single-degree-of-freedom and multi-degrees-of-freedom systems are subjected to typical ground motions excitation. Results illustrate that because of the use of the optimal stiffness ratio of H-infinity optimization and very close value of H-2 optimizations' nominal damping ratio in H-2/H-infinity optimization, H-2/H-infinity optimization shows 'dual characteristics' in different excitation situations. Specifically, the peak response and structural fundamental frequencies' response in displacement frequency response function using hybrid H-2/H-infinity optimal methods are between H-2 and H-infinity optimization, which indicates an excellent and balanced control performance combining the advantages of H-2 and H-infinity optimal solutions. Hence, this hybrid method is more suitable for more complex ground motions excitation to control critical structural responses instead of single characteristic excitation. And the comprehensive vibration control in dynamic time histories analyses can be achieved by this dual characteristic-based optimal strategy. When designing the specific TID, hybrid H-2/H-infinity optimization can be considered as the best choice for its compatibility and high adaptability for complex practical engineering scenarios with random and diverse excitations.