A tuned liquid inerter system for vibration control

This study proposes a novel tuned liquid inerter system (TLIS) that employs a tuned liquid element and an inerter-based subsystem, including damping, stiffness, and inerter elements, to completely utilize their synergy benefits. The stochastic analyses for both damped and undamped structure-TLIS systems are conducted, and the analytical solution to the displacement response is derived for an undamped structure. Using the stochastic response results, the vibration control effect of the proposed TLIS is characterized through an extensive analysis in comparison with classic tuned liquid dampers. A parametric analysis is then performed to investigate the response variation pattern of the structure-TLIS with respect to the changes in TLIS parameters. Inspired by the parametric analysis, an optimal design framework for the most economical condition is developed for the TLIS by simultaneously considering the structural performance and control force. In particular, for a TLIS in the presence of an existing tuned liquid element, the optimal damping and stiffness ratios of the inerter subsystem in the TLIS are derived in an analytical form as the functions of tuned liquid mass and inertance to ensure structural responses are minimized. Moreover, the corresponding design procedure and examples are provided to validate the effectiveness of the proposed TLIS and design methods. It is concluded that the employment of the inerter-based subsystem in the TLIS can substantially improve the structural performance and reduce the displacement response of the tuned liquid in comparison with the classic tuned liquid damper for a given liquid mass. The optimal design of the TLIS can satisfy the target structural performance demands despite optimizing control cost. Simultaneously, the function of the tuned liquid element is partly substituted by the added inerter element, which implicitly facilitates the minimization of the physical mass of the TLIS to achieve lightweight-based control.