Vibrations of a conductive string in a nonstationary magnetic field with account taken of two nonlinear factors

We consider vibrations of a conductive string with fixed ends in a magnetic field whose induction is a given function of time. Two nonlinear factors are taken into account simultaneously: the variation of the tension of the string depending on the displacement and the magnetostrictive effect. It is shown that, in the case of a periodically changing magnetic field, the nonlinear factors can compensate each other, and the problem is reduced to the study of linearized parametric vibrations.