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 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 …

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 addresses a detailed literature review on non-linear modes of vibration and its
role in obtaining more efficient reduced-order models, as compared to those obtained by …

In this paper, post-buckling and nonlinear vibration analysis of geometrically imperfect
beams made of functionally graded materials (FGMs) resting on nonlinear elastic foundation …

In this paper, a new modal superposition method based on a hybrid mode shape concept is
developed for the determination of steady state vibration response of nonlinear structures …

The purpose of this paper is to present efficient and accurate analytical expressions for large
amplitude free vibration and post-buckling analysis of unsymmetrically laminated composite …

In this paper, nonlinear vibration and post-buckling analysis of beams made of functionally
graded materials (FGMs) resting on nonlinear elastic foundation subjected to thermo …

In this paper, non-linear vibration and post-buckling analysis of beams made of functionally
graded materials (FGMs) rest on a non-linear elastic foundation subjected to an axial force …

Theoretical and experimental modal analysis, ie, the computation of vibration modes from a
mathematical model and from experimental data, respectively, is quite sophisticated and …