Analysis of 3:1 internal resonance of a rigid-flexible coupling antenna system with three degrees of freedom

Abstract

This paper investigates the nonlinear dynamic behavior of a spatially deployable antenna’s rigid-flexible coupling structure. Firstly, a three-degree-of-freedom T-beam structure model consisting of a rigid manipulator and a symmetrical antenna is established. By applying the Lagrange equation and the assumed modes method, the governing nonlinear dynamics equations for the T-beam’s in-plane motion are formulated. Subsequently, the system’s nonlinear dynamic behavior under 3:1 internal resonance conditions is investigated employing the matrix-form multi-scale methodology. The general expression of the analytical solution of the system under 3:1 the internal resonance is given and the stability of the approximate solution is analyzed. The criteria governing both periodic and aperiodic motions are established. The amplitude-frequency formulation enables derivation of bifurcation characteristics for the system’s nonlinear mode interactions. Finally, the validity of the approximate solution is confirmed through numerical verification. The results show that there are multiple modal solutions, the numerical solution and the analytical solution are in good agreement with each other. In addition, the effectiveness of the matrix-form multi-scale method for nonlinear dynamics analysis of rigid-flexible coupling systems with multiple degrees of freedom is proved.