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This paper is concerned with the analysis of the self-excited vibrations and forced vibrations of the iced transmission lines. By introducing the external excitation load, the effect of dynamic wind on the nonlinear vibration equations of motion is reflected by vertical aerodynamic force. The approximate analytical solution of the non-resonance, and the amplitude frequency response relation of the principal resonance of the forced self-excited system are obtained by using the multiple scale method. With the increase in excitation amplitude, the nonlinearity of the system is enhanced, and the forced-self-excited system experiences three vibration stages (self-excited vibration, the superposition form of self-excited vibration and forced vibration, forced vibration controlled by nonlinear damping). Among them, the accuracy of the approximate analytical solution decreases with the increase of the nonlinear strength. And the excitation amplitude is greater than the critical value, the quenching phenomenon appear in the forced-self-excited system, and the discriminant formula is derived in this paper. In addition, the frequency of excitation term determines the vibration form of the system. The principal resonance, super-harmonic resonance and subharmonic resonance of the forced-self-excited system are analyzed by using different excitation frequencies. Compared with the principal resonance and the harmonic resonance, the meaningful transition from periodic response to quasi periodic response is easy to appear with the condition of the 1/3-order sub-harmonic and the 3-order super-harmonic. The conclusions would be helpful to the practical engineering of the iced transmission lines. More important, as a combination of Duffing equation and Rayleigh equation, the forced-self-excited system also has high theoretical research value.

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