Decoupling the nonlocal elasticity equations for thermo-mechanical vibration of circular graphene sheets including surface effects

• Vibration analysis of circular graphene sheets under thermo-mechanical loading.
• Both surface and nonlocal effects are taken into account.
• Equation of motion is derived by decoupling the nonlocal constitutive equations.
• Size effects increase by increasing the amount of surface residual stress.

This article deals with the axisymmetric vibration properties of circular single-layered graphene sheet embedded in a polymer matrix under thermo-mechanical loading. Both surface and nonlocal effects are taken into account. To this end, Gurtin–Murdoch continuum elasticity in conjunction with the nonlocal elasticity theory is used to develop a modified continuum plate model for free vibration analysis of the nanoplates. The governing equations are derived by decoupling the nonlocal constitutive equations of Eringen theory in the polar coordinate. Galerkin׳s method is used to obtain the vibration frequencies. To verify the accuracy of the Galerkin results, a differential quadrature (DQ) solution is also developed. Galerkin results are successfully verified with those of the DQ method. A good agreement is also found between the present results and experimental data. Further, in comparison to the available molecular dynamics simulation results, the present formulation with appropriate values of surface and nonlocal parameters provides more accurate results than those by the classical plate model.

The influence of small scale in combination with surface energy and surface residual stress on the vibration characteristics of circular graphene sheets is investigated. The nanoplate is subjected to thermo-mechanical loading.Figure optionsDownload as PowerPoint slide