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

Quantifying stress distribution in ultra-large graphene drums through mode shape imaging