This article presented a nanoscale modified continuum model to investigate the free vibration of functionally graded
(FG) porous nanobeam by using finite element method. The main novelty of this manuscript is presenting effects of four
different porosity models on vibration behaviors of nonlocal nanobeam structure including size effect, that not be discussed
before The proposed porosity models are, uniform porosity distribution, symmetric with mid-plane, bottom surface distribution
and top surface distribution. The nano-scale effect is included in modified model by using the differential nonlocal continuum
theory of Eringen that adding the length scale into the constitutive equations as a material parameter constant. The graded
material is distributed through the beam thickness by a generalized power law function. The beam is simply supported, and it is
assumed to be thin. Therefore, the kinematic assumptions of Euler-Bernoulli beam theory are held. The mathematical model is
solved numerically using the finite element method. Results demonstrate effects of porosity type, material gradation, and
nanoscale parameters on the free vibration of nanobeam. The proposed model is effective in vibration analysis of NEMS
structure manufactured by porous functionally graded materials