In-plane and out of plane free vibration in nano ultra-thin film using a general nonlocal Kirchhoff ultra-thin film model

In this paper, the in-plane and out-plane free vibration of the Kirchhoff nano ultra-thin film are studied. To reveal the altering natures of natural frequencies in nano ultra-thin film, the film is modeled according to the general nonlocal theory (GNT). The film governing equations as well as the characteristics eigenvalues equations are established depending on two different nonlocal parameters. The existence of these different nonlocal parameters causes the model to be able to predict both increase and reduction of stiffness in nano ultra-thin film. Here, the differential quadrature method (DQM) is applied for obtaining the natural frequencies of in-plane and out of plane. An intensive parametric study is carried out on the natural frequencies of nano ultra-thin film. The results reveal that the effect of nonlocal parameters on the frequency parameter is more prominent at the higher aspect ratios.