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.