Membranes of suspended two-dimensional materials show a large variability in
mechanical properties, in part due to static and dynamic wrinkles. As a
consequence, experiments typically show a multitude of nanomechanical resonance
peaks, which makes an unambiguous identification of the vibrational modes
difficult. Here, we probe the motion of graphene nanodrum resonators with
spatial resolution using a phase-sensitive interferometer. By simultaneously
visualizing the local phase and amplitude of the driven motion, we show that
unexplained spectral features represent split degenerate modes. When taking
these into account, the resonance frequencies up to the eighth vibrational mode
agree with theory. The corresponding displacement profiles however, are
remarkably different from theory, as small imperfections increasingly deform
the nodal lines for the higher modes. The Brownian motion, which is used to
calibrate the local displacement, exhibits a similar mode pattern. The
experiments clarify the complicated dynamic behaviour of suspended
two-dimensional materials, which is crucial for reproducible fabrication and
applications
