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Background <p>The conventional tuned mass damper inerter (TMDI) is a passive dynamic vibration absorber that utilizes inertial mass amplification by physically coupling an auxiliary mass directly to the ground through an inerter. However, relatively few studies have focused on deriving exact closed-form solutions for the cross-layer ungrounded TMDI configuration applicable to high-rise structures or long-span bridges. Furthermore, there currently lacks a comprehensive performance evaluation comparing grounded and ungrounded TMDI configurations for both single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF).</p> Purpose <p>This study aims to establish exact closed-form expressions for the optimal parameters of the ungrounded TMDI and to systematically evaluate its vibration control performance in comparison with grounded TMDI and conventional TMD systems.</p> Methods <p>Specifically, optimal tuning and damping parameters for the ungrounded TMDI are derived via H∞ and H2 optimization methods applied to an undamped SDOF primary structure subjected to harmonic force and random base acceleration, respectively. The analytical frequency domain responses of the grounded TMDI, ungrounded TMDI, and conventional TMD are systematically compared. To further explore its control effectiveness for MDOF systems, the ungrounded TMDI is subsequently implemented on a wind-excited 11-degree-of-freedom (DOF) tall slender structure, with the inerter's connection location varied along the height of the primary structure.</p> Results <p>Analytical results show the performance of the ungrounded TMDI is ultimately constrained by the limited relative acceleration of the inerter device for SDOF main structure. However, it generally outperforms the conventional TMD and approaches the performance of the grounded TMDI in MDOF systems.</p> Conclusions <p>The ungrounded TMDI provides a practical and effective vibration control solution for spatially constrained structures. The derived closed-form optimal parameters facilitate efficient design, and the configuration’s performance is highly dependent on the mass ratio, inertance ratio, and inerter connection location.</p>

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Optimal Design and Vibration Control Performance Assessment of Ungrounded Tuned Mass Damper Inerter Configuration

  • 期刊论文

  • 发表日期：

    2025年11月4日

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  • Peiran Fan,
  • Shujin Li,
  • Ling Mao

摘要

Background

The conventional tuned mass damper inerter (TMDI) is a passive dynamic vibration absorber that utilizes inertial mass amplification by physically coupling an auxiliary mass directly to the ground through an inerter. However, relatively few studies have focused on deriving exact closed-form solutions for the cross-layer ungrounded TMDI configuration applicable to high-rise structures or long-span bridges. Furthermore, there currently lacks a comprehensive performance evaluation comparing grounded and ungrounded TMDI configurations for both single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF).

Purpose

This study aims to establish exact closed-form expressions for the optimal parameters of the ungrounded TMDI and to systematically evaluate its vibration control performance in comparison with grounded TMDI and conventional TMD systems.

Methods

Specifically, optimal tuning and damping parameters for the ungrounded TMDI are derived via H∞ and H2 optimization methods applied to an undamped SDOF primary structure subjected to harmonic force and random base acceleration, respectively. The analytical frequency domain responses of the grounded TMDI, ungrounded TMDI, and conventional TMD are systematically compared. To further explore its control effectiveness for MDOF systems, the ungrounded TMDI is subsequently implemented on a wind-excited 11-degree-of-freedom (DOF) tall slender structure, with the inerter's connection location varied along the height of the primary structure.

Results

Analytical results show the performance of the ungrounded TMDI is ultimately constrained by the limited relative acceleration of the inerter device for SDOF main structure. However, it generally outperforms the conventional TMD and approaches the performance of the grounded TMDI in MDOF systems.

Conclusions

The ungrounded TMDI provides a practical and effective vibration control solution for spatially constrained structures. The derived closed-form optimal parameters facilitate efficient design, and the configuration’s performance is highly dependent on the mass ratio, inertance ratio, and inerter connection location.