Primary parametric resonance of an axially accelerating beam subjected to static loads

Primary parametric resonance and stability of an axially accelerating and current-carrying beam subjected to static loads in magnetic field are investigated. The nonlinear magneto-elastic vibration equation is derived. The approximate solution of the static problem and the disturbance deferential equation of the beam with two sides simply supported are obtained. The frequency-response equation of primary parametric resonance is further achieved by a multi-scale method. According to stability conditions, the stability of the steady-state solution is also discussed. By numerical examples, the amplitude versus different parameter curves and the bifurcation diagrams of the amplitude are acquired. The effects of magnetic induction intensity, axial speed, detuning parameter and static loads on nonlinear vibration characteristics are also analyzed.