Dynamic stability of temperature-dependent graphene sheet embedded in an elastomeric medium

This work applies the first-order shear deformation theory (FSDT) to study the dynamic stability of orthotropic temperature-dependent single-layered graphene sheet (SLGS) embedded in a temperature-dependent elastomeric medium and subjected to a biaxially oscillating loading in thermal environment. Possible thermal effects are here considered in the size-dependent governing equations of the problem. These last ones are derived by means of Hamilton’s variational principle combined with the Eringen’s differential constitutive model. Navier’s solution as well as Bolotin’s approach are applied to obtain the dynamic instability region (DIR) of graphene sheet. Thus, a parametric study is carried out to explore the sensitivity of the DIR of the graphene sheet to the temperature variation, the static load factor, the aspect ratio, the foundation type, and the nonlocal parameter (NP). Results indicated that the dimensionless pulsation frequency reduces for increasing values of the temperature and NP, whereas the size effect becomes even more pronounced for increasing temperatures. In addition, the adoption of temperature-dependent mechanical properties, rather than the independent ones, yields a global shift of the DIR to smaller pulsating frequencies. This proves the relevance of the temperature-dependent of the mechanical properties to obtain reliable results, in a physical sense.