Free vibration analysis of FGM nanoplate with porosities resting on Winkler Pasternak elastic foundations based on two-variable refined plate theories

This paper presents a free vibration analysis of functionally graded materials nano-plate resting on Winkler–Pasternak elastic foundations based on two-variable refined plate theories including the porosities effect. The small-scale effects are introduced using the nonlocal elasticity theory with a new shear deformation function. The governing equations are obtained through the Hamilton’s principle. The effect of material property, porosities, various boundary conditions and elastic foundation stiffnesses on free vibration functionally graded materials nanoplate are also presented and discussed in detail. The present solutions are compared with those obtained by other researchers. The results are in a good agreement with those in the literature.