Temperature effects on the vibration and stability behavior of multi-layered graphene sheets embedded in an elastic medium

This communication presents the thermal vibration and stability analysis of the multi-layered graphene sheets (MLGS) modeled as multi-nanoplate system (MNPS) embedded in an elastic medium. Nonlocal elasticity and Kirchhoff-Love plate theories are used for nanoplates, which are considered as orthotropic. Elastic medium is represented by the Winkler's spring model, which couples adjacent nanoplates in MNPS. Governing equations are derived and exact closed form solutions for nonlocal frequencies, critical buckling loads and critical buckling temperature are obtained by using the Navier's and trigonometric methods. The analytical results are validated with the corresponding results in the literature, results obtained via molecular dynamics simulation and numerical method of solution of the system of algebraic equations. To consider the thermal effects on the vibration and stability behavior of MNPS we adopted the coefficient of thermal expansion (CTE) obtained from the experimental results found in the literature. In the parametric study, effects of temperature change, nonlocal parameter, number of nanoplates and change of mediums stiffness on dimensionless nonlocal frequencies, critical buckling load and critical buckling temperature are investigated.