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Dimensionality reduction in mechanical vibratory systems poses challenges fordistributed structures including geometric nonlinearities, mainly because ofthe lack of invariance of the linear subspaces. A reduction method based ondirect normal form computation for large finite element (FE) models is heredetailed. The main advantage resides in operating directly from the physicalspace, hence avoiding the computation of the complete eigenfunctions spectrum.Explicit solutions are given, thus enabling a fully non-intrusive version ofthe reduction method. The reduced dynamics is obtained from the normal form ofthe geometrically nonlinear mechanical problem, free of non-resonant monomials,and truncated to the selected master coordinates, thus making a direct linkwith the parametrisation of invariant manifolds. The method is fully expressedwith a complex-valued formalism by detailing the homological equations in asystematic manner, and the link with real-valued expressions is established. Aspecial emphasis is put on the treatment of second-order internal resonancesand the specific case of a 1:2 resonance is made explicit. Finally,applications to large-scale models of Micro-Electro-Mechanical structuresfeaturing 1:2 and 1:3 resonances are reported, along with considerations oncomputational efficiency.

Model Order Reduction based on Direct Normal Form: Application to Large Finite Element MEMS Structures Featuring Internal Resonance