Journal
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 373, Issue 2051, Pages -Publisher
ROYAL SOC
DOI: 10.1098/rsta.2014.0404
Keywords
nonlinear dynamics; normal forms; modal analysis; cable vibration
Categories
Funding
- Engineering and Physical Sciences Research Council
- [EP/K005375/1]
- [EP/K003836/1]
- EPSRC [EP/K005375/1, EP/K003836/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/K005375/1, EP/K003836/1, 1227535] Funding Source: researchfish
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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 damping and forcing terms are treated as unfolding parameters. The approach is contrasted to the alternative theory of nonlinear normal modes (NNMs) which is argued to be problematic in the presence of damping. The efficacy of the normal form method is illustrated on a model of the vibration of a taut cable, which is geometrically nonlinear. It is shown how the method is able to accurately predict NNM shapes and their bifurcations.
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