Vibration of two-dimensional imperfect functionally graded (2D-FG) porous nano-/micro-beams

This study presents analysis on the vibration behavior of the two-dimensional functionally graded (2D-FG) nano and microbeams which are made of two kinds of porous materials for the first time, based on Timoshenko beam theory. The material of the nano and microbeams is modeled as 2D-FGMs according to the power law. The Eringen's nonlocal elasticity and the modified couple stress theories are used, respectively in case of nano and microbeams. The boundary conditions are considered as clamped (CC), simply supported (SS), clamped-simply supported (CS), and cantilever (CF). The governing equations are solved using the generalized differential quadrature method (GDQM). The effects of FG power indexes along length and thickness are studied along each other and also exclusively. The parametric studies are presented for functionally graded along thickness (FG), functionally graded along length (AFG) and 2D-FG, porous and perfect, micro/nanobeams under different boundary conditions.