Forced vibration analysis of functionally graded beams using nonlocal elasticity

A forced vibration analysis of functionally graded (FG) nanobeams is considered based on the nonlocal elasticity theory. The solution is obtained by using Navier method for various shear deformation theories. The material properties of the FG nanobeam vary through the thickness direction according to a simple power law. Effects of the nonlocal parameter, different material composition and length-to-thickness ratio of considered element on the vibration and the effect of frequency ratio and different dynamic loading conditions on dimensionless maximum deflection and mode shapes of FG nanobeam are investigated. As a result the dynamic behavior of the FG nanobeam is influenced by the nonlocal effects. The dynamic deflections obtained by the classical (local) theory are smaller than obtained by the nonlocal theory due to the nonlocal effects.