Evaluation of optimum length scale parameters in longitudinal wave propagation on nonlocal strain gradient carbon nanotubes by lattice dynamics

Abstract

Longitudinal wave propagation in carbon nanotubes has been investigated by using Rayleigh-Bishop rod model and nonlocal strain gradient elasticity theory in the present study. Size dependent governing equation of motion has been obtained with variational formulation. Validation of the proposed model has been achieved with developed lattice dynamics model which considers neighborhood interaction. Least squares approach has been used in addition to the traditional calibration methodology. Number of atomic interactions, shear strain and rotary inertia effects have important effects on the calibration of scale parameters. Present results could help to continuum modeling of carbon nanotubes with accurate scale parameters.