Mathematics & Physics 2017, 10(1), 36–39 УДК 537.9 Nonlinear Magnetoelastic Dynamics of the Ferrite Plate Fanur F. Asadullin Sergey M.Poleshchikov Dmitriy A. Pleshev∗ Saint-Petersburg state forest technical university Institutskiy, 5, St-Petersburg, 194021 Russia Leonid N.Kotov Vladimir V. Vlasov† Syktyvkar State University Oktyabskiy, 55, Syktyvkar, 167000 Russia Vladimir G. Shavrov Vladimir I. Shcheglov‡ Institute of Radioengineering and Electronics RAS Mohovaya, 11, Moscow, 125009 Russia Received 16.08.2016, received in revised form 21.10.2016, accepted 15.11.2016 The present work deals with investigation of features of a magnetization vector of nonlinear precession and elastic displacements close to ferromagnetic resonance in normal magnetized ferrite plate. <...> The processes of frequency division and frequency multiplication were considered in the research. <...> Problem of excitation of ultrasound oscillations by use of alternating magnetic field in normal magnetized plate is considered in the paper. <...> Processes of parametric excitation and related losses can be prevented by choosing this geometry[1, 2]. <...> The present work deals with investigation of the features of processes of alternating field frequency division and frequency multiplication close to ferromagnetic resonance. 1. <...> The problem is solved in a Cartesian coordinate system Oxyz. <...> The plane Oxy of the coordinate system coincides with the plane of the plate. <...> The coordinate axes are parallel to the edges of the cube crystallographic cell. <...> The center of the coordinate system O is in the center of the plate, so that the plate planes coordinates are z = ±d/2. <...> We consider only excitement of the transverse elastic oscillations. ∗dpleshev@gmail.com †vlasovv78@mail.ru ‡vshcheg@cplire.ru ⃝ Siberian Federal University. <...> Nonlinear Magnetoelastic Dynamics of the Ferrite Plate Assuming that the total energy density of the plate U in the field ⃗ 0m2 z +2c44(u2 xy +u2 H = {hx;hy;H0} equals the sum of magnetic, elastic and magnetoelastic energy densities, we obtain: U = −M0hxmx −M0hymy −M0H0mz +2πM2 yz +u2 where ⃗ M/M0 is normalized magnetization vector, M0 is the saturation magnetization. <...> The initial equations for the system are the Landau-Lifshitz-Gilbert equation and the equam = ⃗ tions for the elastic displacement vector components ux <...>