Two-degree-of-freedom Nonlinear System in Narrow-band Random Excited
He Qun(1), Xu Wei(1), Rong Haiwu(2), Fang Tong(1)
(1 Northwestern Polytechnical University, Xi'an 710072) (2 Foshan University, Guangdong 528000)

Abstract: The two-to-one internal resonance and the principal resonance of a two-degree-of-freedom nonlinear system to narrow-band random parametric excitation are investigated. The method of multiple scales is used to determine the equations of modulation of amplitude and phase. The behavior and stability of steady state response are studied by means of qualitative analyses. The effects of band width and magnitudes of deterministic and random excitations are analyzed. The theoretical analyses are verified by numerical results. Theoretical analyses and numerical simulations show that the intensity of the random excitation increase, the nontrivial steady state solution may change form a limit cycle to a diffuse d limit cycle. Under some conditions the system may have two steady state solutions, and saturation and jumps may exist.
Keywords: Two-degree-of-freedom nonlinear system, 2:1 internal resonance, principal resonance, multiple scale methods, saturation, jump.