Nonlinear Dynamical Analysis of a Circular Truss Antenna in Thermal Environments

Abstract

This paper investigates the nonlinear dynamics of the circular truss antenna with considering the thermal effect. The first-order shear deformation shell theory and the Hamilton’s principle are used to establish the mechanical model for the circular truss antenna system. The motion governing equation is derived for the equivalent circular cylindrical shell. For interest in 1:2:3 internal resonances, the continuous system of nonlinear partial governing differential equation of motion is truncated into a three-degree-of-freedom system of ordinary differential equation including quadratic and cubic nonlinearities. From the averaged equations obtained by the method of multiple scales, numerical simulations are presented to investigate the effects of the thermal excitation on the nonlinear responses of the truss antenna system. Bifurcation diagram, phase portraits, time histories, power spectra and max Lyapunov exponents are used to get the numerically results. It is found that there exist period doubling bifurcations, periodic motions and chaotic motions in the system. The numerical results show that the thermal excitation has significant influence on the nonlinear dynamical behaviors of the circular truss antenna system. The findings in this paper is also useful for the nonlinear vibration control of the shell structure.