This paper aims at reviewing nonlinear methods for model order reduction in structures with
geometric nonlinearity, with a special emphasis on the techniques based on invariant …

This survey paper contains a review of the past and recent developments in system
identification of nonlinear dynamical structures. The objective is to present some of the …

The concept of nonlinear normal modes (NNMs) is discussed in the present paper and its
companion, Part II. Because there is virtually no application of the NNMs to large-scale …

We propose a unified approach to nonlinear modal analysis in dissipative oscillatory
systems. This approach eliminates conflicting definitions, covers both autonomous and time …

The direct computation of the third-order normal form for a geometrically nonlinear structure
discretised with the finite element (FE) method, is detailed. The procedure allows to define a …

The direct parametrisation method for invariant manifolds is used for model order reduction
of forced-damped mechanical structures subjected to geometric nonlinearities. Nonlinear …

This paper reviews the recent advances in computational methods for nonlinear normal
modes (NNMs). Different algorithms for the computation of undamped and damped NNMs …

In order to build efficient reduced-order models (ROMs) for geometrically nonlinear
vibrations of thin structures, a normal form procedure is computed for a general class of …

The definition of a non-linear normal mode (NNM) as an invariant manifold in phase space
is used. In conservative cases, it is shown that normal form theory allows one to compute all …

A method for modal analysis of non-linear and non-conservative mechanical systems is
proposed. In particular, dry-friction nonlinearities are considered although the method is not …