Nonlinear dynamic analysis of ring truss antenna equivalent to the cylindrical shell with thermal excitation

Abstract In this paper, the nonlinear dynamic analysis of the circular truss equivalent to the cylindrical shell under the influence of the thermal excitation and the damping coefficient are studied. The annular truss structure is equivalent to the cylindrical shell structure based on the previous equivalent process, and the nonlinear dynamic equations of the equivalent cylindrical shell considering the effect of thermal excitation are established by using the first-order shear deformation theory. The natural frequencies and modes of the equivalent cylindrical shell are analyzed by the finite element method, and the frequency ratio between modes is calculated. Considering the fixed boundary condition of the equivalent cylindrical shell in the generatrix direction, the torsional mode function and the bending mode function of the equivalent cylindrical shell are selected by the Chebyshev polynomial approximation method and are truncated by Galerkin method. Based on the nonlinear ordinary differential equations of two degrees of freedom, the amplitude-frequency responses, bifurcation, and chaotic characteristics of the system are analyzed. The results show that under the influence of thermal excitation, the motions of the system are complex, and when the excitation amplitude is large, the system appears chaotic motion. The damping coefficient limits the possibility of complex motions of the system. With the influence of the damping coefficient, the motion of the system tends to be stable.