  By calculating a Casimir energy for the acoustic phonons of Graphene, we find
some temperature-dependent corrections for the pretension of a Graphene sheet
suspended on a trench. We obtain values of the order of few mN/m for these
corrections in fully as well as doubly clamped Graphene on a narrow trench with
one nanometer width, at room temperature. These values are considerable
compared to the experimental values, and can increase the fundamental resonance
frequency of the Graphene. The values of these corrections increase by
increasing the temperature, and so they can be utilized for tuning the Graphene
pretension.
