Nonlinear dynamics of a foldable multibeam structure with one to two internal resonances

Nonlinear dynamics of a foldable multibeam structure subjected to a base excitation with one to two internal resonances are investigated in this paper. The nonlinear partial differential governing equations of the multibeam structure is derived by Hamilton's principle. To identify the existing one to two internal resonance for a foldable multibeam structure, the first two natural frequencies of the foldable multibeam structure versus the folding angle are calculated and validated by the finite element method. The characteristic of the one to two internal resonances are illustrated by the dynamic response of the multibeam structure. The modulation equations for the steady state motion of the foldable multibeam structure under this internal resonance condition are obtained by the multiple scales method. The approximation solution derived from the modulation equation is compared with the numerical solution obtained from the original motion equation. A comprehensive study of the nonlinear dynamics of the foldable multibeam structure is performed by considering two cases of harmonic excitation. The saturation and jumping phenomena are observed for the foldable multibeam structure.