H closed-form solution of tuned mass damper enhanced with negative stiffness element (TMD-NS) for structural vibration control

Shaodong Jiang, Kaiming Bi, Ruisheng Ma, Kun Xu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

1 Citation (Scopus)

Abstract

Negative stiffness element has been applied to improve the control performance of tuned mass dampers (TMDs) recently, and two tuned mass dampers enhanced with negative stiffness (TMD-NS) element, namely KDamper (Without loss of generality, it is referred to as TMD-NS I in the present study) and Extended KDamper (EKD, TMD-NS II), have been developed. Previous studies have demonstrated the control effectiveness of TMD-NS I and II. However, there still exist some issues to be addressed: (1) previous studies normally optimize TMD-NS via the intricate and time-consuming numerical methods, the analytical solutions for the optimal design parameters of TMD-NS II remain unknown; (2) a comprehensive and exhaustive evaluation that compares the control effectiveness of TMD-NS I and II is absent from existing literature. To fill these research gaps, this study derives closed-form optimum solutions for TMD-NS II using the H approach. The control effectiveness of TMD-NS I and II in suppressing the seismic responses of structures is investigated systematically. Specifically, the analytical model of an undamped SDOF system equipped with TMD-NS I or II is first developed within a unified framework, and corresponding dynamic equations of motion are formulated. Subsequently, the optimal parameters of TMD-NS I and II are derived based on the classical “fixed-point” theory. Based on the derived optimal parameters, the control effectiveness of TMD-NS I and II are examined by using a damped SDOF system subjected to harmonic excitations and real earthquake ground motions. Finally, a 5-storey isolated benchmark building model is adopted to further investigate the effectiveness of TMD-NS in the seismic protection of engineering structures. The results reveal that the derived closed-form solutions are accurate in capturing the optimal parameters of TMD-NS. In addition, both the optimized TMD-NS I and II outperform the conventional TMD in reducing the seismic responses of structures. Furthermore, TMD-NS I proves more effective in reducing the absolute acceleration of the isolated building, whereas TMD-NS II demonstrates better performance in mitigating the isolating deformation. In a nutshell, both the TMD-NS I and II are highly effective alternatives to conventional TMDs, showcasing superior performance in vibration reduction and robustness.

Original languageEnglish
Article number118510
JournalJournal of Sound and Vibration
Volume586
DOIs
Publication statusPublished - 15 Sept 2024

Keywords

  • Closed-form optimum solutions
  • Control effectiveness
  • Extended KDamper
  • Isolated structures
  • KDamper

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Acoustics and Ultrasonics
  • Mechanical Engineering

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