The railgun system is an electromechanical coupled nonlinear system. Here, considering the electromagnetic force nonlinearity of the rail, the electromechanical coupled nonlinear dynamic equations for the rail are proposed. Using these equations, the nonlinear vibrating frequencies of the railgun system and their changes along with the system parameters are investigated. The amplitude frequency characteristics of the rail are discussed. The results show that the electromagnetic nonlinearity should be considered for a small stiffness of the elastic foundation, small distance between the two rails, and a large rail current. The results can be used for dynamic performance design of the railgun system.

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