Higher-Order Invariant Manifold Parametrisation of Geometrically Nonlinear Structures Modelled with Large Finite Element Models

In this contribution we present a method to directly compute asymptotic expansion of invariant manifolds of large finite element models from physical coordinates and their reduced-order dynamics on the manifold. We show the accuracy of the reduction on selected models, exhibiting large rotations and internal resonances. The results obtained with the reduction are compared to full-order harmonic balance simulations obtained by continuation of the forced response. We also illustrate the low computational cost of the present implementation for increasing order of the asymptotic expansion and increasing number of degrees of freedom in the structure. The results presented show that the proposed methodology can reproduce extremely accurately the dynamics of the systems with a very low computational cost.