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In this paper, a new magneto-electro-elastic functionally graded Timoshenko microbeam model is developed by using the variational formulation. The new model incorporates the extended modified couple stress theory in order to describe the microstructure effect. The power-law variation through the thickness direction of the two-phase microbeams is considered. By the direct application of the derived general formulation, the static bending and free vibration behavior of the newly developed functionally graded material microbeams are analytically determined. Parametric studies qualitatively demonstrate the microstructural effect as well as the magneto-electro-elastic multi-field coupling effect. The proposed model and its classic counterpart produce significant differences for thin graded magneto-electro-elastic Timoshenko microbeams. The thinner the microbeam is, the larger the difference becomes.

On the Bending and Vibration Analysis of Functionally Graded Magneto-Electro-Elastic Timoshenko Microbeams