Parametric-primary resonance of current-carrying ferromagnetic beam in coupled magnetic-temperature fields

A differential equation is derived to analyze the current-carrying ferromagnetic beam in coupled magnetic-temperature fields by means of Galerkin method. Melnikov's function is used to get the necessary critical condition for the chaotic motion of the system in primary resonance. In this system, the phenomenon of chaotic motion couldn't be found. Based on the multiple scales method for nonlinear vibration analysis, the first approximation solutions and the stability corresponding to steady state solutions of the parametric-primary resonance system are obtained. Numerical analysis results show that the temperature can change the internal frequency and the value of amplitude obviously.