Dynamic characteristics and vibration reduction performance of a novel Bi‑TRMD

A novel bidirectional tuned rolling mass damper （Bi-TRMD）device is proposed，and its dynamic characteristics and vibration reduction performance are investigated. The device achieves the performance goal of bidirectional vibration reduction for a tuned rolling mass damper with a single concave structure. First，the Bi-TRMD device is introduced，and its three-dimensional（3D）mechanical model is established. The motion equations of the model are derived using the Gibbs-Appell equation，and a trajectory prediction method for the sphere and structure within the model is developed. This method demonstrates that the rolling motion of the sphere around orthogonal axes is nearly independent within a limited range，enabling the simplification of the 3D model into a two-dimensional（2D）model. The accuracy of this simplification is validated through case analysis. The vibration reduction parameters are optimized using the 2D model and Den Hartog theory，leading to the derivation of mathematical expressions for the optimal frequency ratio and damping ratio. Subsequently，the bidirectional vibration reduction performance of the Bi-TRMD is analyzed. The results show that under white noise excitation， the Bi-TRMD achieves a bidirectional peak acceleration reduction rate that is 9. 92% and 7. 79% higher than that of translational tuned mass dampers（TMD） with the same mass. These findings demonstrate that the proposed Bi-TRMD effectively achieves two-directional vibration reduction with a single concave structure，offering superior vibration reduction performance.