Symmetry-breaking dynamics of a flexible hub-beam system rotating around an eccentric axis

The dynamic analysis on the asymmetrical structures is challenging in the orbit design, attitude adjustment and vibration control of the practical spatial structures. Due to the inevitable manufacturing/assembling errors, the rotational axis of a hub could not be always coincided with its neutral symmetry axis, which leads to an eccentric centrifugal force. This force may enhance the coupling effect of the system, which inspired us to investigate the nonlinear symmetry-breaking dynamics caused by an eccentric rotational axis of a flexible hub-beam system in the present work. First, a simplified coupling nonlinear dynamic model for the flexible hub-beam system rotating around an eccentric axis is proposed based on the Hamiltonian variational principle and continuum mechanics. Then, an innovative complex structure-preserving numerical iteration method is proposed to solve the nonlinear coupling dynamic equations including ordinary differential equations (ODEs) and partial different equations (PDEs). The method is constructed as a bidirectional transmission algorithm between a symplectic Runge-Kutta scheme for ODEs and a generalized multi-symplectic scheme for PDEs. The numerical results show that the eccentricity can lead to the nonlinear dynamics, in forms of the energy evolution of the system, the rotation angular velocity of the hub and the transverse displacement of the flexible beam, which are verified by the results of the finite element method partly. The complex structure-preserving iteration method proposed in this paper gives a new way to investigate the nonlinear coupling dynamics of the asymmetrical structure.