Nonlinear dynamic analysis of parametrically excited space cable-beam structures due to thermal loads

• A general thermo-elastic coupled nonlinear dynamic model is proposed.
• Nonlinear analysis under simultaneous parametric and internal resonance is investigated.
• The parametric excitation caused by thermal loads is considered.
• Analytical forms of responses and nonlinear power flows are proposed.

The objective of this study is to analytically investigate the nonlinear response and nonlinear power distribution of parametrically excited space cable-beam structures under the effects of simultaneous internal and external resonances. The general coupled thermo-elastic equations of cable-beam structures considering geometrically nonlinearity of cables are firstly developed using the finite element method. Linear modal analysis is then performed to decouple the nonlinear differential equations, and yields a complete set of system quadratic/cubic coefficients in modal coordinates. By the method of multiple scales, the first order asymptotic analysis under 1:2 internal resonance and primary resonance is accomplished. Based on acquired stable solutions, the analytical forms of nonlinear nodal and elemental power flows are further proposed. The nonlinear phenomena of a planar parametrically excited cable-beam structure, such as the bending of response curve, jump phenomena, instability regions, saddle-node bifurcation are verified and the corresponding power distribution is explored by means of numerical analysis.