Direct computation of nonlinear mapping via normal form for reduced-order models of finite element nonlinear structures

The direct computation of the third-order normal form for a geometrically nonlinear structure discretised with finite element (FE) method, is detailed. procedure allows to define mapping in order derive accurate reduced-order models (ROM) relying on invariant manifold theory. proposed reduction strategy and simulation free, sense that it pass from physical coordinates (FE nodes) coordinates, describing dynamics an invariant-based span phase space. number master modes ROM not priori limited since complete change coordinate proposed. underlying theory ensures quality predictions thanks invariance property reduced subspace, together their curvatures space accounts nonresonant couplings. method applied beam 3D elements shows its ability recovering internal resonance at high energy. Then fan blade model investigated correct prediction given by ROMs are assessed discussed. A approximate aggregate value damping, takes into account damping coefficients all slave modes, also using Rayleigh as input. Frequency-response curves blades then exhibited, showing accuracy method.