  Suspended drums made of 2D materials hold potential for sensing applications.
However, the industrialization of these applications is hindered by significant
device-to-device variations presumably caused by non-uniform stress
distributions induced by the fabrication process. Here we introduce a new
methodology to determine the stress distribution from their mechanical
resonance frequencies and corresponding mode shapes as measured by a laser
Doppler vibrometer (LDV). To avoid limitations posed by the optical resolution
of the LDV, we leverage a unique manufacturing process to create ultra-large
graphene drums with diameters of up to 1000 um. We solve the inverse problem of
a F\"oppl--von K\'arm\'an plate model by an iterative procedure to obtain the
stress distribution within the drums from the experimental data. Our results
show that the generally used uniform pre-tension assumption overestimates the
pre-stress value, exceeding the averaged stress obtained by more than 47%.
Moreover, it is is found that the reconstructed stress distributions are
bi-axial, which likely originates from the transfer process. The introduced
metholodogy allows one to estimate the tension distribution in drum resonators
from their mechanical response and thereby paves the way for linking the used
fabrication processes to the resulting device performance.
