The dynamic behaviors of a relative-rotation nonlinear dynamic system with cubic coupled terms are studied. First, the dynamic equation of coupled system with nonlinear elastic force and generalized friction and harmonic excitation is deduced. The approximate solution of coupled unautonomous equation under harmonic excitation is obtained by the method of multiple scales. The effect of coupled terms on system resonance is analyzed in respect of principal resonance and internal resonance. The singularity stability of bifurcation function of principal resonance is studied by singularity theory, and the transfer concourse and topological structure of bifurcation function are obtained.