Stability Analysis and Nonlinear Vibrations of the Ring Truss Antenna with the Six-Dimensional System

Purpose The large-scale deployable space antennas(LDSA) generate complex nonlinear vibrations when it is in service in the aerospace. The stability and nonlinear vibrations of the ring truss antenna with the six-dimensional system for the first time in this paper. Methods The Galerkin method is used to truncate the equation of nonlinear governing motion equations of the equivalent composite laminated cylindrical shell model. Considering the case 1:2:3 internal resonances, the multi scales method was used to obtain the six-dimensional averaged equation of the model. From the averaged equation, the frequency response function was solved to analyze the resonance response characteristics. Meanwhile, the stability of the high-dimensional nonlinear system is studied using the method of characteristic root conditions. Results Based on the six-dimensional polar coordinate equations, the three degrees of freedom frequency response functions of the equivalent cylindrical shell structure are obtained. In the case of strong coupling, the system has soft and hard spring characteristics. The type of characteristic root and conditions for hopf bifurcation can be obtained by solving the characteristic equation. Through numerical simulation, it is verified that the system exist chaotic motion. Conclusions Through resonance response analyses, it is found that the coupling factors, perturbation parameters and the thermal excitation can effect the resonance response. The six-dimensional hyper-chaotic system appear hopf bifurcation when the characteristic roots meet certain conditions.