One-to-two internal resonance in two-degrees-of-freedom nonlinear system with narrow-band excitations

Response of two-degrees-of-freedom nonlinear system to narrow-band random parametric excitation is investigated. The method of multiple scales is used to determine the equations of modulation of amplitude and phase. The effect of detunings and amplitude are analyzed. Theoretical analyses and numerical simulations show that the nontrivial steady-state solution may change form a limit cycle to a diffused limit cycle as the intensity of the random excitation increase. Under some conditions, the system may have two steady-state solutions.