Surface effect on vibration characteristics of bi-directional functionally graded nanobeam using Eringen’s nonlocal theory

Abstract A nonlocal model capturing the surface and size effects has been proposed to investigate the vibration behavior of bi-directional functionally graded nanobeam. The material properties of nanobeam are assumed to vary as per the power-law distribution in both the thickness and length directions. For the analysis, surface and size effects have been incorporated by employing the Gurtin-Murdoch surface theory and Eringen’s nonlocal theory, respectively. Using Hamilton’s principle, the governing equation of motion and corresponding boundary conditions have been derived based on the Euler–Bernoulli beam theory. The resulting differential equations have been solved for frequencies by implementing the differential quadrature method. The effect of considering the beam with surface layers and varying values of other parameters on the frequency parameter has been discussed. The results have been verified with the published literature. It is remarkable to report that the surface effect plays an important role in the case of bi-directional functionally graded material.