Vibrations of a conductive string in a nonstationary magnetic field under presence of two nonlinear factors

Abstract

We consider vibrations of a conductive string with fixed ends in a magnetic field. Induction of the magnetic field is a preassigned function of time. Two nonlinear factors are taken into account simultaneously: the variation of string tension with displacement and the magnetostrictive effect. It is shown that, in the case of a periodic magnetic field, the nonlinear factors can compensate each other and the problem can be reduced to studying the linearized parametric vibrations.

Original language	English
Pages (from-to)	600-604
Number of pages	5
Journal	Journal of Applied and Industrial Mathematics
Volume	11
Issue number	4
DOIs	https://doi.org/10.1134/S1990478917040184
Publication status	Published - 1 Oct 2017

Keywords

conductive string
nonstationary magnetic field
parametric vibrations
transversal magnetostriction

ASJC Scopus subject areas

Industrial and Manufacturing Engineering
Applied Mathematics

Access to Document

10.1134/S1990478917040184

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title = "Vibrations of a conductive string in a nonstationary magnetic field under presence of two nonlinear factors",

abstract = "We consider vibrations of a conductive string with fixed ends in a magnetic field. Induction of the magnetic field is a preassigned function of time. Two nonlinear factors are taken into account simultaneously: the variation of string tension with displacement and the magnetostrictive effect. It is shown that, in the case of a periodic magnetic field, the nonlinear factors can compensate each other and the problem can be reduced to studying the linearized parametric vibrations.",

keywords = "conductive string, nonstationary magnetic field, parametric vibrations, transversal magnetostriction",

author = "Tomilin, {A. K.} and Kuril{\textquoteright}skaya, {N. F.}",

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N2 - We consider vibrations of a conductive string with fixed ends in a magnetic field. Induction of the magnetic field is a preassigned function of time. Two nonlinear factors are taken into account simultaneously: the variation of string tension with displacement and the magnetostrictive effect. It is shown that, in the case of a periodic magnetic field, the nonlinear factors can compensate each other and the problem can be reduced to studying the linearized parametric vibrations.

AB - We consider vibrations of a conductive string with fixed ends in a magnetic field. Induction of the magnetic field is a preassigned function of time. Two nonlinear factors are taken into account simultaneously: the variation of string tension with displacement and the magnetostrictive effect. It is shown that, in the case of a periodic magnetic field, the nonlinear factors can compensate each other and the problem can be reduced to studying the linearized parametric vibrations.

KW - conductive string

KW - nonstationary magnetic field

KW - parametric vibrations

KW - transversal magnetostriction

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