Discrete layer solution to free vibrations of functionally graded magneto-electro-elastic plates

Natural frequencies of orthotropic magneto-electro-elastic graded composite plates are determined using a discrete layer model with two different approaches. In the first, the functions describing the gradation of the materials properties through the thickness of the plate are incorporated into the governing equations. In the second approach, the plate is divided into a finite number of homogeneous layers. The model is validated by comparing the natural frequencies of a simply supported Al/ZrO2 graded square plate with the exact solution. Excellent agreement is obtained. Rectangular plates with different boundary conditions, aspect ratios, and made of different types of composite materials are also considered: Al/ZrO2 and BaTiO3/CoFe2O4 plates for which the volume fraction of the phases change as a function of the z coordinate, graphite/epoxy plates with the orientation of the fibers changing through the thickness of the plate, and plates having an exponential variation of the material properties. Applicability of the proposed model is not limited to specific boundary conditions and gradation functions.