Assessing the effects of 2D magnetic field and porosity on the bending and wave propagation in FG nanoplates embedded in an elastic medium

This study examines the bending and wave propagation in porous functionally graded (FG) nanoplates rested on the Winkler–Pasternak foundation using a four variable refined sinusoidal plate theory taking into account the two-dimensional magnetic field. The small size effect is taken into account by using the non-local elasticity theory. Porosity-dependent material properties of the porous FG nanoplate are defined to vary consistently through the thickness direction by a modified power law. From Maxwell's magnetic equations, the body force (Lorentz force) is deduced, which is applied to each particle of the structure. Hamilton's principle of variation is used to derive the equations of motion. These governing equations are solved to study the bending and wave propagation analyses of the porous FG nanoplates. The dispersion relation between frequency and wave number is obtained analytically. Numerical examples are presented to verify the accuracy of the present model by comparing it with the solutions given in the literature. Extensive numerical discussions are introduced for bending and waves in the porous FG nanoplates including the impacts of different parameters, like the magnetic parameter, power-law index, porosity factor, nonlocal parameter, plate aspect-ratio, wave number, and the side-to-thickness ratio as well as elastic foundation parameters. (author)