Free vibration characteristics of nonlocal viscoelastic nano-scaled plates with rectangular cutout and surface effects

In the present study, the viscoelastic free vibration behavior of nano-scaled plates is studied by employing a finite element method based on the two-phase nonlocal integral theory. Various boundary conditions, surface effects and cutouts have been assumed. The principle of total potential energy is used for developing the nonlocal finite element method, and the classical plate theory is assumed to derive the formulations. By numerically solving the eigenvalue problem, which has been obtained by the variational principle, the complex eigenvalues of free vibration of the viscoelastic nano-scaled plates are acquired. The current results are compared with those available in the literature and those obtained by commercial finite element software, and the influences of the nonlocal parameter, viscoelastic parameter, geometrical parameters (e.g. cutout and size), surface effects and different boundary conditions on the complex eigenvalues are studied. It is noted that the current method is able to handle quite versatile boundary conditions and geometries like cutouts, which are rather difficult (or impossible) to be tackled by employing other methods available in most researches.