Vibration analysis of embedded biaxially loaded magneto-electrically actuated inhomogeneous nanoscale plates

In this research, a free vibration study of a biaxially compressed magneto-electro-elastic functionally graded (MEE-FG) nanoplate resting on an elastic substrate is carried out according to a trigonometric plate formulation. Spatially graded MEE properties of the nanoplate are described according to a power-law distribution. Eringen’s nonlocal elasticity model is utilized to incorporate the small-scale influences. The distributions of magneto-electrical potentials in the thickness direction are considered as a combination of cosine and linear variations. The governing equations of the present plate model are obtained employing Hamilton’s principle. Some admissible functions are introduced to satisfy different boundary conditions and solving these equations. It is indicated that vibration frequencies of the MEE-FG nanoplate are dramatically affected by biaxial compression, magnetic potential, electric voltage, elastic substrate, small-scale parameter, and material gradation.