Structural Engineering and Mechanics

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Cost-effectiveness dynamics and vibration of soft magnetoelastic plate near rectangular current-carrying conductors

  • Received : 2021.09.20
  • Accepted : 2023.06.21
  • Published : 2023.10.25
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Abstract

Cost-effective high precision hybrid elements are presented in a hierarchical form for dynamic analysis of plates. The costs associated with controlling the vibrations of ferromagnetic plates can be minimized by adequate determination of the amount of electric current and magnetic field. In the present study, the effect of magnetic field and electric current on nonlinear vibrations of ferromagnetic plates is investigated. The general form of Lorentz forces and Maxwell's equations have been considered for the first time to present new relationships for electromagnetic interaction forces with ferromagnetic plates. In order to derive the governing nonlinear differential equations, the theory of third-order shear deformations of three-dimensional plates has been applied along with the von Kármán large deformation strain-displacement relations. Afterward, the nonlinear equations are discretized using the Galerkin method, and the effect of various parameters is investigated. According to the results, electric current and magnetic field have different effects on the equivalent stiffness of ferromagnetic plates. As the electric current increases and the magnetic field decreases, the equivalent stiffness of the plate decreases. This is a phenomenon reported here for the first time. Furthermore, the magnetic field has a more significant effect on the steady-state deflection of the plate compared to the electric current. Increasing the magnetic field and electric current by 10-times results in a reduction of about 350% and an increase of 3.8% in the maximum steady-state deflection, respectively. Furthermore, the nonlinear frequency decreases as time passes, and these changes become more intense as the magnetic field increases.

Keywords

References

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