Size-dependent static bending, free vibration and buckling analysis of simply supported flexomagnetic nanoplates

Kirchhoff plate model is applied to investigate the flexomagnetic effect in a simply supported piezomagnetic nanoplate. Based on Hamilton’s variational principle, strain gradient theory and Kirchhoff plate model, governing differential equations and corresponding boundary conditions are established. By employing Navier’s method, governing differential equations are transformed into algebraic equations and thus an analytical solution for size-dependent static bending, free vibration and buckling analysis of flexomagnetic nanoplate is established. In comparison and validation with available investigations, a good agreement is found. The remarkable impact of flexomagnetic coupling over the piezomagnetic response has been noted for thin nanoplates with low dimensions, which wanes as the geometric dimensions are increased. Influences of aspect ratio, flexomagnetic coefficient and scale parameter on bending deformation, free vibration and stability are discussed in detail.