Geodesic
Vibrations of a~conductive string in a~nonstationary magnetic field with account taken of two nonlinear factors
Sibirskij žurnal industrialʹnoj matematiki, Tome 20 (2017) no. 4, pp. 61-66

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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.
Keywords: conductive string, nonstationary magnetic field, transverse magnetostriction, parametric vibrations. 
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     author = {A. K. Tomilin and N. F. Kurilskaya},
     title = {Vibrations of a~conductive string in a~nonstationary magnetic field with account taken of two nonlinear factors},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
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A. K. Tomilin; N. F. Kurilskaya. Vibrations of a~conductive string in a~nonstationary magnetic field with account taken of two nonlinear factors. Sibirskij žurnal industrialʹnoj matematiki, Tome 20 (2017) no. 4, pp. 61-66. http://geodesic.mathdoc.fr/item/SJIM_2017_20_4_a7/