Non-linear normal modes, invariance, and modal dynamics approximations of non-linear systems View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1995-10

AUTHORS

Nicolas Boivin, Christophe Pierre, Steven W. Shaw

ABSTRACT

Non-linear systems are here tackled in a manner directly inherited from linear ones, that is, by using proper normal modes of motion. These are defined in terms of invariant manifolds in the system's phase space, on which the uncoupled system dynamics can be studied. Two different methodologies which were previously developed to derive the non-linear normal modes of continuous systems — one based on a purely continuous approach, and one based on a discretized approach to which the theory developed for discrete systems can be applied-are simultaneously applied to the same study case-an Euler-Bernoulli beam constrained by a non-linear spring-and compared as regards accuracy and reliability. Numerical simulations of pure non-linear modal motions are performed using these approaches, and compared to simulations of equations obtained by a classical projection onto the linear modes. The invariance properties of the non-linear normal modes are demonstrated, and it is also found that, for a pure non-linear modal motion, the invariant manifold approach achieves the same accuracy as that obtained using several linear normal modes, but with significantly reduced computational cost. This is mainly due to the possibility of obtaining high-order accuracy in the dynamics by solving only one non-linear ordinary differential equation. More... »

PAGES

315-346

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf00045620

DOI

http://dx.doi.org/10.1007/bf00045620

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1086035939


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