Graphene is a 2D latticed sheet, made up of carbon atoms. Covalent sp 2 bondings between carbon atoms in graphene, form an array of hexagons. Graphene sheet may be found as a single layer or bilayer types. In fact, graphene may be regarded as the most popular kind of double-orthotropic nanoplate (DONP). Due to its amazing mechanical and electrical charactertistics, garphene has found a wide range of applications or potential applications. For example the Young’s modulus of graphene is of order 1(TPa); the stiffest known material. Therefore many studies have been recently carried out to investigate mechanical behavior of DO. In this study the mechanical buckling and vibration of a double-orthotropic rectangular nanoplate which is resting on an elastic foundation, is studied. The elastic foundation is modeled by the two parameters Pasternak model, which is obtained by adding a shear layer to the Winkler model. Eringen’s nonlocal elasticity theory was utilized to derive constitutive equations. The nonlocal theory accounts for the small-scale effects occuring at the nanoscale. Also, two-variable refined plate theory was employed to derive the governing equations of buckling and vibration. In this theory takes the transverse shear effects into account via assuming a parabolic distribution for the transverse shear strains through the plate thickness. Therefore, the results obtained from this theory are more accurate than those obtained from the kashida; TEXT-ALIGN: justify; LINE-HEIGHT: normal; TEXT-KASHIDA: 0%; TEXT-INDENT: 1cm; MARGIN: 0cm 0cm 0pt; mso-layout-grid-align: none" Also it was observed that the effect of Pasternak stiffness is much more than the other stiffnesses. Moreover Vanderwalls stiffness may affect the buckling load only in out-of-phase. In vibration analysis, it was also shown that the natural frequency decreases as the aspect ratio of the nanoplate increases or the support’s stiffness decreases. Finally two variable refined theory and first order shear deformation theory were compared and a very good agreement between the results of these theories was observed. Keywords: Double-orthotropic nanoplate,Mechanical buckling, Free vibration, Nonlocal theory,Two variable refined plate theory,Differential quadrature method.
