Andronov-Hopf bifurcations, Pomeau-Manneville intermittent chaos and nonlinear vibrations of large deployable space antenna subjected to thermal load and radial pre-stretched membranes with 1:3 internal resonance

Abstract

Abstract Andronov-Hopf bifurcations, Pomeau-Manneville intermittent chaos and nonlinear vibrations of the large deployable space antenna (LDSA) subjected to the thermal load with the case of 1:3 internal resonance are studied for the first time. The frequencies and vibration modes of the LDSA are analyzed by using the finite element method. It is found that there may exist an approximate threefold relationship between the fourth-order and first-order frequencies of the LDSA. The LDSA is simplified to a composite laminated equivalent cylindrical shell clamped along a generatrix and with the radial pre-stretched membranes at two ends subjected to the thermal load. Considering the case of 1:3 internal resonance, four-dimensional nonlinear averaged equations are obtained by using the method of multiple scales. The amplitude-frequency response curves and amplitude-force response curves are obtained for the LDSA subjected to the thermal load through the prediction-correction continuation algorithm. The fold bifurcation and Andronov-Hopf bifurcation points are located on these resonant response curves. The equivalent model of the LDSA has the hardening spring characteristics. The thermal load has very significant influences on the stability of the LDSA. The nonlinear dynamics of the equivalent model for the LDSA are investigated by using the fourth-order Runge-Kutta algorithm. These nonlinear dynamic behaviors are described by the bifurcation diagrams, waveforms, phase plots, and Poincare maps. The periodic doubling bifurcation and Pomeau-Manneville type intermittent chaos appear in this nonlinear dynamical system. According to the topological evolution of the phase trajectories, the phase-locking phenomenon and a special evolution path of the chaotic attractors are found.