Asymptotic Computation of Invariant Manifolds of large Finite Element structures with Geometric Nonlinearities

A high order direct parametrisation of invariant manifolds is exploited to operate dimen-
sionality reduction for vibrating structures subjected to geometric nonlinearities. The method defines a nonlinear coordinate change between the nodal degrees-of-freedom and the normal coordinates, hence expressing the dynamics in an invariant-based span of the phase space. The method is applied to study micro-electro-mechanical systems (MEMS) subjected to geometric nonlinearities and internal resonance. Remarks on the computational performance are reported to highlight the efficiency of the technique.