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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]