Multifield gradient theory on vibration of FG magneto-electro-elastic microbeams resting on Pasternak foundation

A novel multifield gradient theory for magneto-electro-elastic (MEE) materials including strain, electric and magnetic potentials, and inertia gradients is presented. Then, free vibration of the functionally graded MEE (FGMEE) microbeams based on the multifield gradient theory is investigated. The material properties of the FGMEE microbeams change continuously and symmetrically along the thickness direction in terms of a power-law distribution. Four kinds of length scale parameters are adopted to capture the size effect of the FGMEE microbeams. Based on the Hamilton’s principle, the equations of motion for the FGMEE microbeams are derived, which are solved subsequently by differential quadrature method. In the numerical examples, the effects of length scale parameters, electric and magnetic loadings, foundation parameters, and material gradient index on the natural frequency are analyzed and discussed in detail.