OICC Press Journal of Solid Mechanics 2008-7683 4 2 2012 06 30 Small Scale Effect on the Vibration of Orthotropic Plates Embedded in an Elastic Medium and Under Biaxial In-plane Pre-load Via Nonlocal Elasticity Theory 128 143 EN M Mohammadi Department of Engineering, Ahvaz branch, Islamic Azad university M Goodarzi Department of Engineering, Ahvaz branch, Islamic Azad university M Ghayour Department of Mechanical Engineering, Isfahan University of Technology S Alivand Department of Engineering, Ahvaz branch, Islamic Azad university Journal Article 2012 06 30 In this study, the free vibration behavior of orthotropic rectangular graphene sheet embedded in an elastic medium under biaxial pre-load is studied. Using the nonlocal elasticity theory, the governing equation is derived for single-layered graphene sheets (SLGS). Differential quadrature method (DQM) has been used to solve the governing equations for various boundary conditions. To verify the accuracy of the present results, a Navier’s approach is also developed. DQM results are successfully verified with those of the Navier’s approach. The results are subsequently compared with valid result reported in the literature. The effects of the small scale, pre-load, Winkler and Pasternak foundations and material properties on natural frequencies are investigated. The results are shown that with the decrease of in-plane pre-loads the curves isotropic and orthotropic non-dimensional frequency in approaches close to each other.