An inerter-system chain and energy-based optimal control of adjacent single-degree-of-freedom structures

Because of the limited land resources and preference of centralized services, more structures are often built close to each other, correspondingly yielding a demand that mitigates the dynamic responses of adjacent structures. Utilizing the intrinsic potential of the inerter to improve structural energy performances, an inerter-system chain is proposed for the adjacent singledegree-of-freedom structures, which forms a novel configuration featuring the reduction in input energy transmitted to the adjacent structures. The inerter-system chain is realized by two end-placed inerter-dashpot dampers and inter-placed springinerter-dashpot elements arranged in parallel. Stochastic energy balance analysis is conducted to derive a closed-form energy equation that reveals the energy basis of the inerter-system chain. An energy-based and bi-objective optimization strategy is developed with simultaneous consideration of displacement and energy performances, particularly easy-to-use design formulae being derived. The findings of this study show that a complete inerter-system chain exhibits a significant multi-reduction in the structural displacement, shear force, and dissipation energy burden. Particularly, the effectiveness of reducing the input power and vibrational energy transmitted into the entire structures counts on the series inerter-chain, which differentiates the proposed chain from alternative layouts. The proposed energy-based design framework is capable of minimizing the energy dissipation cost, with target displacement control demand satisfied.