A novel vibration-reduction motion planning method for fast moving mass traveling along flexible structures

This study concerns dynamic behaviors and vibration reduction of the flexible structure subjected to a moving mass traveling on it. The mathematical model of a simply supported beam carrying a moving particle mass is derived according to the Hamilton's principle. Dynamic responses of the substrate flexible beam under various traveling profiles are analyzed and implied that the moving mass would induce evident motion-induced dynamic deflection and residual vibration, and such effects highly depend on the motion profiles. The key novelty of this paper is proposing a data-driven, high-efficiency vibration-reduction motion planning approach to the moving mass. Such a motion planning approach is imposed by quintic spline curves and Kriging surrogate model-based optimization algorithm combined with the expected improvement infilling-sampling criterion. The optimization results reveal that a favorable motion profile can be found by using only 2 waypoints and within approximately 100 samplings. In the case of minimization of the transient deflection amplitude, lower transient deflection, which is even lower than the static value, can be obtained using the optimized motion profile. In the case of minimization of residual vibration energy, a smooth deformation history of the substrate beam can be produced, while the vibration energy has also been significantly reduced. Using the minimization of residual vibration energy as the objective function is primarily recommended in the motion planning issue. Improved motion profiles with varied terminal times could also be obtained and proved the robustness of the proposed optimization approach. The proposed data-driven optimization approach could provide a feasible and high-efficiency way to design a favorable traveling profile for a moving mass system from the perspective of structural vibration reduction.