Surface and Nonlocal Effects on Coupled In-Plane Shear Buckling and Vibration of Single-Layered Graphene Sheets Resting on Elastic Media and Thermal Environments using DQM

Abstract

AbstractIn this article, surface and nonlocal effects are explored in the analysis of buckling and vibration in rectangular single-layered graphene sheets embedded in elastic media and subjected to coupled in-plane loadings and thermal conditions. The small-scale and surface effects are taken into account using the Eringen's nonlocal elasticity and Gurtin-Murdoch's theory, respectively. Using the principle of virtual work, the governing equations considering small-scale are derived for the nanoplate bulk and surface. The differential quadrature method (DQM) is utilized for the solution of the relevant problems and the results are validated against Navier's solutions. The impacts of the nonlocal parameter, Winkler and shear elastic moduli, temperature rise, boundary conditions, and the in-plane biaxial, uniaxial, and shear loadings on the surface effects of buckling and vibration are investigated. Numerical results show that increasing nonlocal parameter leads to enhanced surface effects on both buckling and vibration. This is in contrast to those reported elsewhere. Moreover, increasing in-plane loads are observed to enhance surface effects on vibration. On the other hand, the nonlocal parameter is observed to have more pronounced effects on shear buckling and vibration of plates subjected to coupled in-plane shear loads than those subjected to biaxial and uniaxial loads. This is while surface effects have greater impacts on biaxial buckling and vibration of nanoplates than on shear buckling and vibration.