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 …

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 …

Dimensionality reduction in mechanical vibratory systems poses challenges for distributed
structures including geometric nonlinearities, mainly because of the lack of invariance of the …

The surface and nonlocal effects on the nonlinear flexural free vibrations of elastically
supported non-uniform cross section nanobeams are studied simultaneously. The …

Since the founding theory established by G. Floquet more than a hundred years ago,
computing the stability of periodic solutions has given rise to various numerical methods …

This work addresses the large amplitude nonlinear vibratory behavior of a rotating cantilever
beam, with applications to turbomachinery and turbopropeller blades. The aim of this work is …

Non-intrusive methods have been used since two decades to derive reduced-order models
for geometrically nonlinear structures, with a particular emphasis on the so-called STiffness …

The objective of this contribution is to compare two methods proposed recently in order to
build efficient reduced-order models for geometrically nonlinear structures. The first method …

In this article, we address the model identification of nonlinear vibratory systems, with a
specific focus on systems modeled with distributed nonlinearities, such as geometrically …