Multi-pulse jumping double-parameter chaotic dynamics of eccentric rotating ring truss antenna under combined parametric and external excitations

Abstract

We study the multi-pulse jumping double-parameter homoclinic orbits and chaotic dynamics of the eccentric rotating ring truss antenna under combined the parametric and external excitations for the first time. Considering combined the parametric and external excitations, the averaged equations of the eccentric rotating circular cylindrical shell are obtained in the case of the primary parametric resonance-1/2 sub-harmonic resonance and 1:2 internal resonance by using the perturbation analysis. From the averaged equation, the theory of normal form is applied to find the explicit expression of the eccentric rotating circular cylindrical shell under combined the parametric and external excitations. Based on the extended Melnikov method, we study the multi-pulse double-parameter homoclinic bifurcation and chaos of the eccentric rotating circular cylindrical shell under combined the parametric and external excitations and also estimate the double-parameter chaotic threshold. Numerical simulations are utilized to study double-parameter chaotic dynamic behaviors of the eccentric rotating circular cylindrical shell under combined the parametric and external excitations based on the double-parameter Lyapunov exponents. When one of the excitations is constant, it is found that the temperature parametric excitation directly decides the occurrence of the chaotic motion and the external excitation determines the paths to chaos. It is also known that the topology shapes of the chaotic motions are similar when the excitations corresponding to the chaotic motions change in a small range. Otherwise, there exists the obvious difference of the shapes for the topological structure of the double-parameter chaotic motions in the eccentric rotating circular cylindrical shell.