In the present work, as an extension to , an autonomous geometrically nonlinear
reduced order model for the study of dynamic solutions of complex rotating structures
is developed. In opposition to the classical finite element formulation for geometrically
nonlinear rotating structures that considers small linear vibrations around the static
equilibrium, nonlinear vibrations around the pre-stressed equilibrium are now considered.
For that purpose, the linear normal modes are used as a reduced basis for the construction
of the reduced order model. The stiffness evaluation procedure method (STEP)  is
applied to compute the nonlinear forces induced by the displacements around the static
equilibrium. This approach enhances the classical linearised small perturbations hypothesis
to the cases of large displacements around the static pre-stressed equilibrium. Furthermore,
a comparison between the steady solution given by HHT-α  and the Harmonic Balance
Method (HBM)  is carried out. The proposed reduced order models are evaluated for
a rotating beam case study.