On bending, buckling and free vibration analysis of 2D-FG tapered Timoshenko nanobeams based on modified couple stress and surface energy theories

In this study, the static bending, buckling, and free vibration behaviors of two-dimensional functionally graded (2D-FG) tapered micro/nanobeams are modelled and analyzed. For the first time, the nonclassical equations of motion and corresponding boundary conditions of 2D-FG beam are simultaneously derived in the framework of the modified couple stress and Gurtin-Murdoch surface elasticity theories in conjunction with the Timoshenko beam theory....