Optimal design based on analytical solution for storage tank with inerter isolation system

An optimal design method based on closed-form analytical solutions is proposed for a liquid storage tank with inerter isolation system. The storage tank is modeled accounting for the flexibility of the tank wall, and isolated by the inerter isolation system composed of an inerter, a damping element, and a spring element connected between the same two terminals in parallel. The stochastic response of the storage tank with inerter isolation system, in terms of sloshing height and isolation displacement, is derived in closed form under the assumption of white-noise excitation. These analytical results are then used in an extensive parametric analysis to investigate the response variation pattern with respect to changes in the parameters of inerter system. In the extremum condition that represents the most efficient parameter set of inertance-mass ratio and damping ratio for response mitigation, an optimal design method is developed by exploiting a performance-demand-oriented design philosophy. The optimal design formulae of the inerter system are derived on the basis of target sloshing height mitigation ratio in analytical form. Moreover, a series of examples are provided to verify the proposed analytical design formulae and design criterion. Based on results from response history analysis under both artificial and natural ground motion records, the design method proves to be effective to meet the desired demand of sloshing height response, while simultaneously reducing base shear force and isolation displacement. The derived analytical design formulae are practical and convenient for preliminary design purposes and substantially explain the mechanism of inerter system for vibration control of liquid storage tank.