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Changes in the natural frequency of a ferromagnetic rod in a magnetic field due to magnetoelastic interaction

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Abstract

Based on the magnetoelastic generalized variational principle and Hamilton’s principle, a dynamic theoretical model characterizing the magnetoelastic interaction of a soft ferromagnetic medium in an applied magnetic field is developed in this paper. From the variational manipulation of magnetic scale potential and elastic displacement, all the fundamental equations for the magnetic field and mechanical deformation, as well as the magnetic body force and magnetic traction for describing magnetoelastic interaction are derived. The theoretical model is applied to a ferromagnetic rod vibrating in an applied magnetic field using a perturbation technique and the Galerkin method. The results show that the magnetic field will change the natural frequencies of the ferromagnetic rod by causing a decrease with the bending motion along the applied magnetic field where the magnetoelastic buckling will take place, and by causing an increase when the bending motion of the rod is perpendicular to the field. The prediction by the mode presented in this paper qualitatively agrees with the natural frequency changes of the ferromagnetic rod observed in the experiment.

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Authors and Affiliations

  1. Key Laboratory of Mechanics on Western Disasters and Environment, Lanzhou University, Lanzhou, 730000, P. R. China

    Xing-zhe Wang  (王省哲)

Authors
  1. Xing-zhe Wang  (王省哲)
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Correspondence to Xing-zhe Wang  (王省哲).

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Communicated by GUO Xing-ming

Project supported by the National Natural Science Foundation of China (No. 10502022) and the Program for New Century Excellent Talents in University (NCET-050878)

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Wang, Xz. Changes in the natural frequency of a ferromagnetic rod in a magnetic field due to magnetoelastic interaction. Appl. Math. Mech.-Engl. Ed. 29, 1023–1032 (2008). https://doi.org/10.1007/s10483-008-0806-x

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  • DOI: https://doi.org/10.1007/s10483-008-0806-x

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