Modelling and stability of magnetosoft ferromagnetic plates in a magnetic field

The equations of magnetoelasticity of magnetoelastic plates remain three dimensional even after adopting the Kirchhoff hypothesis. In the present work, two-dimensional equations of magnetoelasticity are obtained for a magnetoelastic ferromagnetic plate of finite size. In the general case the compone...

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Bibliographic Details
Published in:Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 2001-09, Vol.457 (2013), p.2063-2077
Main Authors: Hasanyan, D. J., Piliposyan, G. T.
Format: Article
Language:English
Subjects:
Boundary conditions
Critical values
Dirichlet problem
Equations of motion
Ferromagnetic Plate
Magnetic fields
Magnetic permeability
Magnetoelasticity
Magnetostatics
Mathematical functions
Natural satellites
Small Parameter
Stability Expansion
Vibration
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Summary:The equations of magnetoelasticity of magnetoelastic plates remain three dimensional even after adopting the Kirchhoff hypothesis. In the present work, two-dimensional equations of magnetoelasticity are obtained for a magnetoelastic ferromagnetic plate of finite size. In the general case the components of the induced magnetic field inside and outside the plate and the amplitudes of lateral vibrations are connected through both the equations of motion and the boundary conditions. This connection essentially complicates the problem of lateral vibrations of magnetoelastic plates of finite size. Assuming that the magnetic susceptibility is very large compared with unity, the solution of the magnetostatics problem in the interior and exterior domains is constructed through asymptotic series with respect to the reciprocal of the magnetic susceptibility. As a result, a system of separated problems with corresponding boundary conditions is obtained, connected by recurrent relations. This allows us to obtain an analytical representation for the components of the excited magnetic field in the case of a very thin plate. The problem of determining the lateral vibrations of magnetosoft ferromagnetic plates of finite size in a magnetic field reduces to a twodimensional singular integrodifferential equation. Using the Galerkin method, the determination of the frequencies reduces to an infinite system of algebraic equations with a normal-type determinant.
ISSN:1364-5021
1471-2946
DOI:10.1098/rspa.2001.0799