Free vibration of a bi-directional imperfect functionally graded nanobeams based on nonlocal Timoshenko beam theory

In this paper, the free vibration of a bi-directional functionally graded (2D-FG) nanobeams is investigated by the finite element method. Nanobeams are made of two kinds of porous materials. The material properties of 2D-FG nanobeams are assumed to vary in both axial and thickness directions according to a power law . Based on Eringen's nonlocal elasticity theory, the governing equations of motion are derived.