  We carried out measurements on nanoelectromechanical systems based on
multilayer graphene sheets suspended over trenches in silicon oxide. The motion
of the suspended sheets was electrostatically driven at resonance using applied
radio-frequency voltages. The mechanical vibrations were detected using a novel
form of scanning probe microscopy, which allowed identification and spatial
imaging of the shape of the mechanical eigenmodes. In as many as half the
resonators measured, we observed a new class of exotic nanoscale vibration
eigenmodes not predicted by the elastic beam theory, where the amplitude of
vibration is maximum at the free edges. By modeling the suspended sheets with
the finite element method, these edge eigenmodes are shown to be the result of
non-uniform stress with remarkably large magnitudes (up to 1.5 GPa). This
non-uniform stress, which arises from the way graphene is prepared by pressing
or rubbing bulk graphite against another surface, should be taken into account
in future studies on electronic and mechanical properties of graphene.
