Analytical solution of cross- and angle-ply nano plates with strain gradient theory for linear vibrations and buckling

Vibrations and buckling of Kirchhoff nano plates are investigated using second-order strain gradient theory. The Navier displacement field has been considered for two different sets of boundary conditions and stacking sequences. Different geometries and material properties for isotropic, orthotropic cross- and angle-ply laminates are considered, and numerical simulations are discussed in terms of plate aspect ratio and non local ratio. A comparison with the classical analytical solution is provided whenever possible for buckling loads and fundamental frequencies.