Bending, buckling and vibration of axially functionally graded beams based on nonlocal strain gradient theory

A size-dependent inhomogeneous beam model, which accounts for the through-length power-law variation of a two-constituent axially functionally graded (FG) material, is deduced in the framework of the nonlocal strain gradient theory and the Euler–Bernoulli beam theory. By employing the Hamilton principle, the equations of motion and boundary conditions for size-dependent axially FG beams are deduced. A material length scale parameter and a...