Size dependent FEM model for Bi-directional functionally graded nano-beams

Abstract Analysis and numerical results for non-local free vibration behavior of bi-directional functionally graded nano-beams have been presented via Eringen’s theory. The beam is graded exponentially along axial direction and according to a power law in thickness direction. The governing differential equation for such an Euler-Bernoulli beam has been obtained using Hamilton principle. The finite element formulation of resulting equation for clamped-clamped boundary conditions has been developed. Employing MATLAB, the natural frequencies for first three modes have been obtained to study the effect of various parameters on vibration characteristics of considered nano-beams. A validation of the results has been presented.