Structure-Preserving Analysis on Flexible Hub-Beam with Hollow Tapered Cross Section

Purpose: Considering the manipulators applied in the space missions, a flexible hub-beam model with a hollow tapered cross section is concerned based on the classic hub-beam model in this paper. Method: The dynamic equations describing the coupling behaviors between the rotation of the hub and the vibration of the flexible beam with a hollow tapered cross section are proposed first. Then, combining the symplectic precise integration method for the rotation of the hub and the approximate multi-symplectic method for the transverse vibration of the flexible hollow tapered cross-section beam, a complex structure-preserving iteration approach is constructed to investigate the dynamic response of the concerned coupling dynamic system. Results and Conclusions: The effects of the taper ratio and the hollow ratio of the beam on the dynamic response of the coupling system are investigated in the numerical simulations in detail. From the numerical results presented in this paper, it can be found that, with the increase of the taper ratio or the decrease of the hollow ratio of the beam, both the stable rotation angular speed of the hub and the stable vibration amplitude of the beam decrease, which provide some guidance for the structural design and the structural optimization of the manipulator employed in space structure when the dynamic properties of the system is taken into account. The above numerical results are verified by the tiny relative errors of the total energy of the system indirectly.