Vibrations and Stability of Magnetostrictive Rectangular Plates in a Magnetic Field

In this chapter, based on the linearized three-dimensional equations and surface conditions of magnetoelasticity of magnetostrictive media obtained in the first chapter, the issues of vibration and stability of rectangular thin plates in a magnetic field are investigated. Using Kirchhoff's hypothesis on non-deformable normals, the asymptotic method for integrating linear boundary value problems in a rectangular domain, and the basic principles of the classical theory of thin plates, the three-dimensional problem under consideration is reduced to a two-dimensional one. On this basis, the corresponding problems of oscillation and stability of the considered magnetoelastic stability are formulated and solved and it is shown that: (a) there is a region of change in the geometric parameters of the plate and the magnetostrictive characteristics of its material, where the unperturbed state of the plate is stable at any value of the induction of the external permanent magnetic field; (b) in this region, a magnetic field can lead to a significant increase in the frequency of magnetoelastic oscillations; (c) outside this region, the magnetostrictive effect has a destabilizing effect, leading to a significant decrease in the critical value of magnetic induction (at which the plate loses stability) compared to the indicated critical value obtained in the absence of the magnetostrictive effect; (d) loss of dynamic stability of the plate under the influence of a non-stationary magnetic field is possible; (e) due to taking into account magnetostriction, the layered plate can perform forced oscillations under the influence of a time-harmonic magnetic field; (f) the specified inhomogeneous plate in a non-stationary magnetic field becomes a source of propagation of disturbances.