Magnetic field effect on vibration of a rotary smart size-dependent two-dimensional porous functionally graded nanoplate

In this article, the free vibration of a rotating two-directional functionally graded porous magnetoelastic nanosize circular plate is analytically studied. The presented model incorporates effects of the small-scale parameter and external magnetic loading. In contrast to the previous works, the material properties of the circular nanoplate are considered to be functionally graded in both thickness and radial directions. In addition, the magnetic actuation is also taken into account in the analysis. By using Hamilton’s principle and employing the modified couple stress theory, the governing equations and boundary conditions are derived based on the first-order shear deformation theory. The derived equations are solved by using the differential quadrature method. The validity of the present analysis is confirmed by comparing the obtained results with the results existed in the literature. A detailed parametric study is conducted to highlight the influences of the boundary conditions type, size dependency, porosity factor, non-dimensional angular velocity, functionally graded power index, initial external magnetic potential, variation form of the material properties, and radius-to-thickness ratio on the non-dimensional natural frequencies of the circular nanoplate.