Trajectory Optimization for Vibration Suppression of a Rotating Flexible Beam with a Moving Mass
Hao Du, Dongping Jin, Jialiang Sun
Abstract: A new trajectory optimization method for vibration suppression of a rotating flexible beam with a moving mass is proposed, in which the variable-length reduced beam element of absolute nodal coordinate formulation (ANCF) in the framework of arbitrary Lagrange-Euler (ALE) is used to represent the time-varying mass. The effects of trajectories, moving mass, and moving time on the dynamic responses are investigated. The results reveal that under identical conditions, varying mass primarily leads to nonlinear vertical stretching of in-plane transverse vibration curves and changes in residual oscillation periods, while the addition of moving time to horizontal stretching of the in-plane transverse vibration curves. It can be concluded that the in-plane transverse vibration of the moving mass exhibits significant dependence on the trajectories of both the moving mass and the rotating beam. In same time, the quintic-polynomial trajectory yields a significantly smoother vibration curve. Compared with other trajectories, the residual vibration amplitude with the un-optimized quintic-polynomial trajectory is on the order of 10–5 m for a 2-meter length of beam, a reduction of one to two orders in magnitude. Afterwards, a trajectory optimization method is developed to optimize the coefficients of the quintic-polynomial trajectories based on genetic algorithm (GA). The optimized results show that a population size of 24 individuals enables the identification of favorable trajectories after approximately 50 iterations. The optimized trajectories exhibit significantly lower residual vibration amplitudes than that of the un-optimized quintic-polynomial trajectory. Although the stochastic distribution of initial populations leads to slight variations in evolutionary histories for identical cases. It demonstrates the effectiveness of the proposed trajectory-optimization method, confirming that trajectory planning alone can successfully suppress structural vibrations. Finally, experiments incorporating a flexible rotating beam with a moving mass are conducted. The experimental and simulation curves can preliminarily verify the accuracy of the dynamic model and the effectiveness of the trajectory optimization method under the premise of similar amplitude and consistent trend.
文章链接：https://www.sciencedirect.com/science/article/pii/S0263823125013424
