Analytical and numerical studies of free vibration frequencies of ferromagnetic plates with arbitrary electric conductance in a transverse magnetic field in the 3D setting

作者：Bagdoev A G^*; Vardanyan A V

来源：Mechanics of Solids, 2008, 43(5): 808-814.

DOI：10.3103/S0025654408050166

The problem on the vibrations of a magnetoelastic ferromagnetic plate was studied in [1-5] from the viewpoint of the averaging approach, i.e., on the basis of the classical Kirchhoff hypothesis. In [6-10], a new approach proposed for elastic plates in [11] was used to derive dispersion relations for magnetoelastic plates. In [10], the 3D approach was used to obtain the ferromagnetic plate vibration frequencies; in the case of a transverse magnetic field, the equations of the perturbed motion of the plates were written out with the initial stresses taken into account [5, 12] but without considering the initial strains. In [13, 14], the problems on the vibrations of conducting plates in a magnetic field were studied.
In the present paper, we derive the dispersion equations, which are asymptotic equations for small magnetic fields and exact equations for the initial stresses and strains related by Hooke's law. The corresponding numerical computations are also performed.

• 出版日期2008-10