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We study circular nanomechanical graphene resonators by means of continuum elasticity theory, treating them as membranes. We derive dynamic equations for the flexural mode amplitudes. Due to geometrical nonlinearity these can be modeled by coupled Duffing equations. By solving the Airy stress problem we obtain analytic expressions for eigenfrequencies and nonlinear coefficients as functions of radius, suspension height, initial tension, back-gate voltage and elastic constants, which we comparedoi:10.1088/0957-4484/24/39/395702 pmid:24008430 fatcat:wlekny4sw5amzcl3ywztur2g7a