free vibration analysis of functionally graded porous nano-‎plates with different shapes resting on elastic foundation

This paper proposes a finite element method (fem) based on a nonlocal theory for analyzing the free vibration of the functionally graded porous (fgp) nano-plate with different shapes lying on the elastic foundation (ef). the fgp materials with two-parameter are the power-law index (k) and the porosity volume fraction (ξ) in two cases of even and uneven porosity. the ef includes winkler stiffness (k1) and pasternak stiffness (k2). some numerical results in our work are compared with other published to verify accuracy and reliability. moreover, the influence of geometric parameters, materials on the free vibration of the fgp nano-plates resting on the ef is comprehensively investigated.