“…The Bernoulli-Euler beam theory considers the following displacement field š(š, š”) = š¢ (š„, š§, š”)š š + š¢ (š„, š§, š”)š š (6) where š š and š š are, respectively, the unit vectors along x-and z-axes; š¢ (š„, š§, š”) and š¢ (š„, š§, š”) indicate the Cartesian components of the displacement field along š„ and š§ axes at time t, expressed as follows As it is well-known, for a Bernoulli-Euler FG nanobeam whose mechanical and physical properties vary along the thickness (z), it can be assumed that the bulk elastic modulus of elasticity, E B = E B (z), the surface modulus of elasticity, E S = E S (z), the residual surface stress, Ļ S = Ļ S (z), the bulk mass density, Ļ B = Ļ B (z), and the surface mass density, Ļ S = Ļ S (z), follow power-law functions as given below [28]…”