Coupled vibration analysis of the spacecraft with the flexible shaft and solar panels assembly

Dynamical characteristics of the spacecraft with flexible components are investigated in this paper. The component consists of a flexible shaft and solar panels, where solar panels are completely fixed on the shaft. A novel power series multiplier polynomial method is proposed to describe the connecting condition between the shaft and solar panels. The deformation and force matching conditions between the one dimensional shaft and two dimensional panels are established, which is the major contribution about the multidimensional combined structure of this study. According to constraining boundary conditions of the shaft and solar panels, the bendingtorsion coupled deformation of the component is expressed. The attitude maneuvering of the central platform and the elastic vibration of the component cause the rigid-flexible coupled effect. Then the discrete dynamical equation of the spacecraft is obtained by using the rigid-flexible coupled modal shapes. The correctness of the proposed method is verified by comparing the natural characteristics with that of the finite element model. The relative error of the higher order frequency is not more than 4%. Numerical results show that the degree of the bending angle polynomial should be at least quadratic to ensure the accuracy of the calculation. The proposed power series multiplier polynomial breaks through the barriers that the traditional Lagrange multiplier cannot express the continuous constraint. It is an effective method to fit the constrained boundary by the polynomial rather than by the discrete multipoint method.