2015
DOI: 10.1098/rsta.2014.0404
|View full text |Cite
|
Sign up to set email alerts
|

The use of normal forms for analysing nonlinear mechanical vibrations

Abstract: A historical introduction is given of the theory of normal forms for simplifying nonlinear dynamical systems close to resonances or bifurcation points. The specific focus is on mechanical vibration problems, described by finite degree-of-freedom second-order-in-time differential equations. A recent variant of the normal form method, that respects the specific structure of such models, is recalled. It is shown how this method can be placed within the context of the general theory of normal forms provided the da… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1
1

Citation Types

5
77
0

Year Published

2015
2015
2024
2024

Publication Types

Select...
5
2

Relationship

2
5

Authors

Journals

citations
Cited by 60 publications
(82 citation statements)
references
References 34 publications
5
77
0
Order By: Relevance
“…By inspection of Eqs. (13) and (14) and of Eqs. (15) and (16), these solutions (in terms of the resonant response) are the in-plane-only mode S1:…”
Section: Backbone Curvesmentioning
confidence: 98%
“…By inspection of Eqs. (13) and (14) and of Eqs. (15) and (16), these solutions (in terms of the resonant response) are the in-plane-only mode S1:…”
Section: Backbone Curvesmentioning
confidence: 98%
“…It has been shown by considering nonlinear normal modes that-in stark contrast to a linear system-a two-degrees-offreedom nonlinear oscillator can exhibit more than two modes of vibration (e.g. Kerschen et al [14] or Neild et al [15]). …”
Section: (A) Behaviour Characterizationmentioning
confidence: 99%
“…Numerous analytical and numerical methods may be used to compute the NNMs of a system [16,17], but here the numerical continuation software AUTO-07p is employed [18]. Figure 2(a) shows five of the NNM branches of the two-mode model of the example system.…”
Section: Nonlinear Normal Modes Of the Beam Modelmentioning
confidence: 99%