Elastic wave phenomenon of nanobeams including thickness stretching effect

The present work deals with an investigation on longitudinal wave propagation in nanobeams made of graphene sheets, for the first time. The nanobeam is modelled via a higher-order shear deformation theory accounts for both higher-order and thickness stretching terms. The general nonlocal strain gradient theory including nonlocality and strain gradient characteristics of size-dependency in order is used to examine the small-scale effects. This model has three-small scale coefficients in which two of them are for nonlocality and one of them applied for gradient effects. Hamilton supposition is applied to obtain the governing motion equation which is solved using a harmonic solution procedure. It is indicated that the longitudinal wave characteristics of the nanobeams are significantly influenced by the nonlocal parameters and strain gradient parameter. It is shown that higher nonlocal parameter is more efficient than lower nonlocal parameter to change longitudinal phase velocities, while the strain gradient parameter is the determining factor for their efficiency on the results.