Application of a generalized matrix averaging method for the calculation of the effective properties of thin multiferroic layers

It is proposed to use a generalized matrix averaging (GMA) method for calculating the parameters of an effective medium with physical properties equivalent to those of a set of thin multiferroic layers. This approach obviates the need to solve a complex system of magnetoelectroelasticity equations. The required effective characteristics of a system of multiferroic layers are obtained using only operations with matrices, which significantly simplifies calculations and allows multilayer systems to be described. The proposed approach is applicable to thin-layer systems, in which the total thickness is much less than the system length, radius of curvature, and wavelengths of waves that can propagate in the system (long-wave approximation). Using the GMA method, it is also possible to obtain the effective characteristics of a periodic structure with each period comprising a number of thin multiferroic layers.

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