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

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 …

This paper is an extension of the previous review, done by the same authors (Mikhlin, Y.,
and Avramov, KV, 2010,“Nonlinear Normal Modes for Vibrating Mechanical Systems …

A rub-impact can bring the impact load and friction force onto the rotor, and in the meantime,
it can also produce the additional effect of changing the stiffness of the rotor system. Past …

The recently developed generalized Fourier–Galerkin method is complemented by a
numerical continuation with respect to the kinetic energy, which extends the framework to …

Two principal concepts of nonlinear normal vibrations modes (NNMs), namely the Kauderer–
Rosenberg and Shaw–Pierre concepts, are analyzed. Properties of the NNMs and methods …

Nonlinear Dynamics represents a wide interdisciplinary area of research dealing with a
variety of “unusual” physical phenomena by means of nonlinear differential equations …

This paper considers the use of numerically constructed invariant manifolds to determine the
response of nonlinear vibratory systems that are subjected to harmonic excitation. The …

A numerical method, based on the invariant manifold approach, is presented for constructing
non-linear normal modes for systems with internal resonances. In order to parameterize the …