Nano-Scaled Plate Free Vibration Analysis by Nonlocal Integral Elasticity Theory

Abstract

In the current study, a finite element method is developed using the principle of total potential energy based on nonlocal integral elasticity theory to investigate the free vibration behavior of nano-scaled plates. The classical plate theory is considered for deriving the formulations of the plate. The eigenvalue problem is extracted by using the variational principle and corresponding natural frequencies of free vibration are obtained. Different boundary conditions and various geometries can now be appropriately analyzed by using the nonlocal finite element method proposed in the current article. The results of the current study are compared with those available in the literature. Then the effects of nonlocal parameters, geometrical parameters, various boundary conditions and surface effects on the free vibration behavior of nano-scaled plates are investigated.