An exact analytical approach for free vibration of Mindlin rectangular nano-plates via nonlocal elasticity

Eringen nonlocal theory is employed in Mindlin plate theory to consider small scale effects on free vibration of rectangular nano-plates. Introducing some auxiliary and potential functions, an exact analytical procedure is applied on the governing equations to decouple the displacement variables. It is believed that this method is new for solving vibration of nano-plates. The solution of natural frequencies is obtained for Levy-type boundary conditions (two opposite edges simply supported and the others arbitrary). In order to confirm the reliability of the method considered, the results are compared with several reported literature. The effect of nonlocal parameter is investigated on natural frequency of the nano-plate for different boundary conditions. Finally the influence of aspect ratio and thickness to length ratio on natural frequency is studied in detail. It is expected that results obtained in this paper serve as an accurate reference in future nano-structures issues.