Nonlinear analysis and experimental investigation of a rigid-flexible antenna system

During the on-orbit service of an deployable antenna, the resonance of the antenna will affect the accuracy of direction. The nonlinear dynamics of a rigid-flexible space antenna is studied under the conditions of two-to-one or three-to-one internal resonance analytically and experimentally. The nonlinear dynamic equations for the planar vibration of the antenna structure with two degrees of freedom are derived via the assumed modes method. Then, the resonance parameter planes are obtained according to the length ratio, the mass ratio and the stiffness of the torsional spring in the antenna system. Afterwards, the method of multiple scales is utilized to obtain the approximate solutions under two-to-one or three-to-one internal resonance. Furthermore, the bifurcation characteristics of the nonlinear normal modes of the antenna system are investigated as well. The results show that more than one nonlinear normal mode exist over a wide range of the detuning parameter. To validate the accuracy of the approximate solution, a numerical solution and an experimental investigation are presented, respectively. The results show that both the numerical and the experimental results agree well with the analytical one.