Equivalent continuum model and nonlinear breathing vibrations of rotating circular truss antenna subjected to thermal excitation

Abstract

This paper focuses on the equivalent continuum model and nonlinear vibrations of a rotating circular truss antenna subjected to the thermal excitation. A rotating equivalent continuum cylindrical shell is proposed to take place of the circular truss antenna through obtaining the static and kinematical equivalence between the beam element and equivalent-plate element. The nonlinear governing equations of the rotating equivalent cylindrical shell are derived by using the first-order shear deformation theory, von Karman nonlinear strains-displacement relation and Hamilton's principle. The accuracy of this model is verified by comparing the dimensionless frequencies obtained by the present method with those in open literature. The influences of the geometric and material parameters and rotating speed on the first two dimensionless natural frequencies are investigated. The obtained results are useful for improvement in the design and optimization of the material parameters and geometry sizes of the rotating circular truss antenna. The case of 1:2 the internal resonance, primary parametric resonance and 1/2 subharmonic resonance of the rotating equivalent cylindrical shell is considered through the method of multiple scales. The frequency-response curves are obtained to study the nonlinear vibrations of the rotating equivalent cylindrical shell. The periodic and chaotic vibrations can be found for the rotating equivalent cylindrical shell subjected to the thermal excitation. The results of this study give useful information to avoid the internal resonance and control the resonant responses of the rotating circular truss antenna.