Nonlinear dynamic analysis near resonance of a beam-ring structure for modeling circular truss antenna under time-dependent thermal excitation

The analysis on the nonlinear dynamics of the circular truss antenna is an important problem for its design and control since its large flexible structure. This paper investigates the nonlinear dynamic behaviors of a beam-ring structure modeling the circular truss antenna subjected to the periodic thermal excitation. Based on describing the displacements and the nonlinear strains of the beam-ring structure, the kinetic energy and potential energy are calculated for the system. Using Hamilton's principle, the nonlinear partial differential governing equations of motion and the boundary conditions are derived for the beam-ring structure. Applying Galerkin's approach, the nonlinear partial governing differential equations of motion for the beam-ring structure are truncated into a two-degree-of-freedom system of the ordinary differential equation including the quadratic nonlinearities. The four-dimensional averaged equation is obtained for the case of the primary resonance and 1:2 internal resonance by using the method of multiple scales. From the averaged equation, numerical simulations are presented to investigate the frequency–response curves and the influences of the thermal excitation on the nonlinear dynamic responses of the beam-ring structure. The numerical results demonstrate that there exist the complex nonlinear dynamic phenomena of the beam-ring structure. The finding phenomena of this paper are helpful for controlling the nonlinear vibrations of the antenna.