Surface and small-scale effects on vibration analysis of a nonuniform nanocantilever beam

The natural frequency of a nonuniform nanocantilever beam with consideration of surface effects is studied using the nonlocal elastic theory. The governing equation of transverse vibration for the nonuniform nanocantilever beam, including both surface and nonlocal effects, is obtained first, and then the Rayleigh–Ritz method is used to determine the natural frequency of the beam. When the nanocantilever beam is assumed to be of uniform cross section and the surface effects are neglected in the analysis, the result is in agreement with the previous study. According to the analysis, the nonlocal and surface effects on frequency of the nonuniform nanocantilever beam are significant.