  We apply the well-established theoretical method developed for geometrical
nonlinearities of micro/nano-mechanical clamped beams to circular drums. The
calculation is performed under the same hypotheses, the extra difficulty being
to analytically describe the (coordinate-dependent) additional stress generated
in the structure by the motion. Specifically, the model applies to
non-axisymmetric mode shapes. An analytic expression is produced for the
Duffing (hardening) nonlinear coefficient, which requires only the knowledge of
the mode shape functions to be evaluated. This formulation is simple to handle,
and does not rely on complex numerical methods. Moreover, no hypotheses are
made on the drive scheme and the nature of the in-plane stress: it is not
required to be of electrostatic origin. We confront our predictions with both
typical experimental devices and relevant theoretical results from the
literature. Generalization of the presented method to Duffing-type
mode-coupling should be a straightforward extension of this work. We believe
that the presented modeling will contribute to the development of nonlinear
physics implemented in 2D micro/nano-mechanical structures.
