Primary parametric resonance of current-carrying conductor

In order to study on nonlinear vibration of current-carrying conductor, a differential equation is established by means of dynamics theory. Based on the method of multiple scales, the first approximate solution and corresponding solution of the primary parametric resonance is obtained. Numerical analysis results show that the amplitude and the topological structure changed with the increase of direct current. The characteristics and laws of the primary parametric resonance excited by the other system parameters such as current, detuning, tension and damping are also analyzed. It has also been found that the natural frequency of the system increases with the increasing tension but decreases with the increasing length.