NONLINEAR-PRIMARY RESONANCE OF AXIALLY MOVING CURRENT-CARRYING BEAMS BETWEEN TWO PARALLEL WIRES

The magneto-elastic primary resonance of an axially moving current-carrying beam is investigated, where the beam move between two parallel and infinite long straight current-carrying wires. According to the principles of an electromagnetic field, the expressions of the electromagnetic force loading on the current-carrying beam is developed. Based on the Hamiltonian principle, the transverse vibration control equations of an axially moving current-carrying beam is derived. The non-dimensional nonlinear differential equation of an axially moving beam is obtained by means of Galerkin method. The approximate analytical solution of first two-order modal nonlinear equation and the primary resonance-amplitude-frequency response equation are derived by means of the multiple scales method. Through computational examples, the resonance amplitude of the axially moving current-carrying beam varying with frequency parameters, current-carrying density, current of wire, and the position variation relationship are obtained. The results show that there is an obvious nonlinear behavior and a great influence on the resonance characteristics of the system when the relevant physical and geometric parameters are changed.