Dynamic analysis and optimal design of a pendulum rotary tuned mass damper for bidirectional control of rotational and translational vibrations

This paper proposes a novel pendulum rotary tuned mass damper (PRTMD), which primarily consists of a mass sphere, a rigid rod, a rigid ring, and a torsional spring. The proposed damper can simultaneously provide both rotational and translational control capabilities to the controlled structure without being constrained by the installation position. A rotational-translational rigid block model that independently incorporates both rotation and translation is developed to evaluate the bidirectional control capability of the proposed PRTMD system, and the parameter optimization criterion for bidirectional control is redefined based on the H ∞ norm. Analysis results demonstrate that, with appropriate parameter configuration, the PRTMD system achieves simultaneous and effective control of both rotation and translation. Additionally, using independent rotational and translational models, the closed-form optimal parameter solutions for the PRTMD system applied separately to rotational and translational control are derived via fixed-point theory, and the dynamic characteristics are highlighted through comparison with unidirectional TMDs. Finally, the control capability of the PRTMD system for complex coupled motion is evaluated using the rocking rigid block model that couples both rotation and translation. The results show that the PRTMD system, possessing bidirectional control capability, exhibits superior overturning suppression for rocking rigid blocks compared to other unidirectional TMDs, can further enhance control performance by increasing the pendulum length and mass, and is applicable to rigid blocks of various slenderness ratios.