Coupling Dynamic Behaviors of Flexible Thin-Walled Tapered Hub-Beam with a Tip Mass

Purpose: The weight-reduction demand requires us to design the space manipulator as a thin-walled tapered beam, which will amplify the vibration of the space manipulator in the carrying process of the operating/capture target to a designed position. A complex structurepreserving approach is employed to investigate the carrying process of the target by using the space manipulator. Method: Combining the symplectic precise integration method with the generalized multi-symplectic method, the complex structurepreserving approach is developed to solve the considered coupling dynamic problem. Firstly, the dynamic equations describing the coupling dynamic problem of the flexible thin-walled tapered hub-beam system are derived. Then, the generalized multi-symplectic formulation with dynamic symmetry-breaking factor is derived for the vibration of the beam, which is discrete by using the Preissmann scheme subsequently. And the rotation of the system will be solved by using the symplectic precise integration method. Results and Conclusions: The numerical results of the stable vibration amplitude of the beam with different tip masses are presented. The contour lines of the stable vibration amplitude of the beam with different tip masses reported in this paper show that the effects of the tip mass on the vibration of the flexible thin-walled tapered beam are remarkable, which provides a criterion on the design of the structural parameters (including the hollow ratio and the tapering ratio) of the space manipulator with a certain vibration limitation of the arm directly.