Determination of neutral axis position and its effect on natural frequencies of functionally graded macro/nanobeams

A modified functionally graded beam theory based on the neutral axis is exploited to investigate natural frequencies of macro/nanobeams. The location of neutral axis is determined, where material properties of FG nanobeams are assumed to vary through the thickness according to a power law. The FG nanobeam is investigated on the basis of the nonlocal Eringen continuum model. The kinematic assumption of nanobeam is proposed according to Euler–Bernoulli beam theory. The finite element method is used to discretize the model and obtain a numerical approximation of the equation of motion. The verification of the model is obtained by comparing the current results with previously published work. Numerical results are presented to show the significance of neutral axis position, the material distribution profile, and nonlocal effect on the fundamental frequencies of nanobeams.