Nonlinear dynamic analysis of space cable net structures with one to one internal resonances

The nonlinear dynamic analysis of cable net structures becomes more and more significant for their space applications required high surface accuracy, especially mesh reflector antennas. In this work, the resonant multi-modal dynamics due to 1:1 internal resonances in the finite-amplitude vibrations of cable net structures subjected to harmonic loads are investigated. The nonlinear dynamic equation of space cable net structures is first developed using the extended Hamilton principle, which belongs to the self-excited vibration with quadratic and cubic nonlinearities. Linear modal analysis is then performed to decouple the nonlinear differential equations, and yields a complete set of system quadratic/cubic coefficients. With the aim of parametrically revealing nonlinear behaviors of space cable net structures, the second-order asymptotic analysis under 1:1 internal resonance is accomplished by the method of multiple scales. The nonlinear phenomena of a planar cable net and cable net reflector, such as the bending of response curve, jump phenomena, instability regions, saddle-node bifurcation, are verified by means of numerical analysis.