Free Vibration Analysis of Nanoplates using Differential Transformation Method

In this paper, a free vibration of nano-plates is investigated considering the small scale parameter. The used rectangular nano-plate is thin and under different boundary conditions. In order to obtain the natural frequencies of the nano-plates, classical plate theory on the basis of non-local theory is used. The governing equation is solved using a semi-analytical method DTM (Differential transformation method). The results for free vibration of those plates are compared with the theoretical data published in the literature. Results show that DTM is a powerful, simple, accurate and fast method for solving equations in comparison with other methods. Nonlocal parameter is very effective in vibration of nano-plates and its influence is different in various boundary conditions. Influence of this parameter in simply supported-clamp boundary condition is higher than other boundary conditions.