Nonlocal beam model and FEM of free vibration for pristine and defective CNTs

Abstract

Abstract The natural frequencies of defective single-walled carbon nanotubes are studied and compared with the values for pristine structures. In order to capture the size-dependent effects in carbon nanotubes, nonlocal stress gradient theory within a Euler-Bernoulli beam model is involved. The analytical computations are compared with finite element analysis of a structural model of carbon nanotubes. The numerical analysis of free vibrations is applied to predict the value of the nonlocal parameter. The eigenfrequencies obtained from finite element analysis are much lower compared with analytical computations of local (classical) beam model. For defective structures having small vacancy, a slight decrease in the eigenfrequencies is observed. All studied boundary conditions indicated the higher the nonlocal parameter is, the lower the natural frequencies are.