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In this present paper, a mini-max optimal design of a non-traditional Tuned Mass Damper with negative stiffness (NTNS-TMD) for damped primary structures is investigated to reduce high amplitudes in the resonant range of vibrations. The differential equation is formulated and the analytical solution of the system is derived. Using the principles of fixed-point theory, the closed-form solution for the optimal tuning coefficient is analytically obtained. Then, the optimal damping ratio and the optimal negative stiffness parameter of the proposed non-traditional TMD with negative stiffness are determined numerically by solving a set of nonlinear equations established using Chebyshev’s equioscillation theorem. Extended simulations are conducted to examine the effectiveness of the optimally designed NTNS-TMD and the sensitivity of the optimal parameters. Finally, the vibration control performance of the proposed configuration is compared with those of two typical TMDs, which were presented by Liu and Pennestri, respectively. The comparison results demonstrate that the non-traditional TMD with negative stiffness significantly enhances vibration control by reducing the dynamic magnification response of damped primary structures.

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Design Parameters and Dynamic Analysis of a Novel High-Performance Tuned Mass Damper with Grounded Negative Stiffness for Vibration Control of Damped Primary Systems

  • 会议论文

  • 发表日期：

    2026年

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  • Okba Abid Charef,
  • Mayada Bouaoun

摘要

In this present paper, a mini-max optimal design of a non-traditional Tuned Mass Damper with negative stiffness (NTNS-TMD) for damped primary structures is investigated to reduce high amplitudes in the resonant range of vibrations. The differential equation is formulated and the analytical solution of the system is derived. Using the principles of fixed-point theory, the closed-form solution for the optimal tuning coefficient is analytically obtained. Then, the optimal damping ratio and the optimal negative stiffness parameter of the proposed non-traditional TMD with negative stiffness are determined numerically by solving a set of nonlinear equations established using Chebyshev’s equioscillation theorem. Extended simulations are conducted to examine the effectiveness of the optimally designed NTNS-TMD and the sensitivity of the optimal parameters. Finally, the vibration control performance of the proposed configuration is compared with those of two typical TMDs, which were presented by Liu and Pennestri, respectively. The comparison results demonstrate that the non-traditional TMD with negative stiffness significantly enhances vibration control by reducing the dynamic magnification response of damped primary structures.