Optimal Design of Tuned Mass-Damper-Inerter for Structure with Uncertain-but-Bounded Parameter

In this study we focus on the H∞ optimization of a tuned mass damper inerter (TMDI), which is implemented on an harmonically forced structure of a single degree of freedom in the presence of stiffness uncertainty. Posed as a min-max optimization problem, its closed-form solutions are analytically derived via an algebraic approach that was newly developed in this work, and ready-to-use formulae of tuning parameters are provided herein for the optimal TMDI (referred to as the TMD). The accuracy of the derived solutions are examined by comparing them with the existing literature and with numerically solved solutions in both deterministic and uncertain scenarios. Our numerical investigation suggested that compared to the classic design, the proposed tuning strategy could effectively reduce the peak vibration amplitude of the host structure in the worst-case scenario. Moreover, its peak vibration amplitude decreases monotonically as the total amount of the tuned mass and inertance increases. Therefore, the incorporation of a grounded inerter in a traditional TMD could render the deteriorated performance of vibration control less important, thereby protecting the primary system against the detuning effect more effectively. Finally, the effectiveness of the proposed design under random excitation is also underlined.

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