Advantages and design of inerters for isolated storage tanks incorporating soil conditions

Inerter-based isolation systems are effective in providing seismic protection for storage tanks. However, the vibration control-oriented mechanism of inerter-based seismic isolation systems on the seismic response of liquid storage tanks remains unclear, with designs limited to rigid base assumptions. Moreover, the objective existence of the soil-structure interaction (SSI) is overlooked. This study contributes to a discovered advantage of the inerter-based isolation system, including the reduction of input energy and precise control of specific or multiple modes of sloshing heights. Furthermore, an advantageous feature-oriented optimal design for storage tanks with an inerter-based isolation system and with the incorporation of soil conditions is proposed in this study. Initially, an analytical model is developed, considering a storage tank with multi-mode sloshing responses and representing SSIs with frequency-dependent stiffness and damping coefficients. Stochastic response analysis is performed, leading to a novel formulation of multi-mode control and an empirical power equation that quantifies the input energy reduction effect. An advantageous feature-oriented optimal design framework, in which the SSI effect, tank geometric parameters, and inerter-based isolation system parameters are implemented, is established through comprehensive parametric analysis. The results demonstrate that the inerter-based isolation system can be intentionally designed to mitigate specific modes of sloshing height, with the inerter effectively reducing the input power of the entire tank. This study emphasizes the importance of incorporating the SSI effect in the seismic analysis and optimal design of inerter-based tanks. Particularly, the inerter-based isolation system designed assuming a rigid base cannot perform as expected due to the SSI effect, significantly resulting in larger seismic responses and energy dissipation burdens. The developed optimal design method guarantees a target base shear force and sloshing height regarding the considered soil condition.