  The effect of the initial uniaxial stress and a surrounding elastic matrix on
the transverse vibration response of a single-layered graphene sheet (SLGS) is
investigated through a theoretical formulation that is based on the nonlocal
Kirchhoff plate theory. The surrounding elastic matrix of the SLGS is modeled
as a foundation of the Pasternak-type. The elliptic partial differential
equation governing the dynamics of the pre-stressed SLGS is solved with the
Rayleigh method. Numerical results from the analyses reveal different level of
sensitivity of the vibration response of the SLGS to changes in the control
parameters of the model. Pareto charts of the effect of the control parameters
in the mathematical model show the shear modulus of the foundation to have the
most dominant influence on the fundamental natural frequency of the SLGS. The
small-scale effect is found to have more pronounced effect on the vibration
response of the SLGS when it is fully clamped at the four edges.
