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The work is devoted to mathematical modeling of vibrations of two-layered magnetoactive plate in a non-stationary magnetic field. Material of one of the layers of the plate is an isotropic magnetostrictive dielectric, and the other one - is made of a dielectric composite material whose electromagnetic properties are equivalent to the properties of a vacuum. Based on the theory of thin plates and on the linearized theory of magnetoelasticity of ferromagnetic bodies, basic equations and boundary conditions are obtained describing the dynamic behavior of magnetoelastic system under consideration. On this basis, the corresponding problem of mathematical physics is formulated, which shows (a) if magnetic field is a stationary, then the plate bends under the action of such fields; (b) if external magnetic field is non-stationary, then it stimulates the forced magnetoelastic vibrations of the plate. Thus, the examined inhomogeneous plate in a harmonic in time magnetic field that becomes a source of perturbation propagation. The angle of reinforcement of the composite layer is included in coefficients of equations and boundary conditions, which significantly affects these phenomena. [ABSTRACT FROM AUTHOR]

In this paper the issues of dynamic stability of three-layered magntostrictive ferromagnetic plate under the action of harmonic in time transversal magnetic field are studied. Having solved the certain problem in this paper it is established, that due to the magnetostrictive properties of plate material it is possible to generate resonant vibrations of parametric type (possibility of loss of dynamic stability) in the examined plate under the action of harmonic in time magnetic field. The influences of heterogeneity and magnetostrictive properties of the plate on the exaamined areas is studied, also. [ABSTRACT FROM AUTHOR]

Based on the theory of magnetoelasticity of dielectric ferromagnetic solids and on the classical theory of thin elastic plates, the main equations and boundary conditions are obtained describing the behavior of small perturbations in the three-layered magnetostrictive plates in the presence of a transverse magnetic field. [ABSTRACT FROM AUTHOR]