An upper bound for validity limits of asymptotic analytical approaches based on normal form theory - ENSTA Paris - École nationale supérieure de techniques avancées Paris Accéder directement au contenu
Article Dans Une Revue Nonlinear Dynamics Année : 2012

An upper bound for validity limits of asymptotic analytical approaches based on normal form theory

Résumé

Perturbation methods are routinely used in all fields of applied mathematics where analytical solutions for nonlinear dynamical systems are searched. Among them, normal form theory provides a reliable method for systematically simplifying dynamical systems via nonlinear change of coordinates, and is also used in a mechanical context to define Nonlinear Normal Modes (NNMs). The main recognized drawback of perturbation methods is the absence of a criterion establishing their range of validity in terms of amplitude. In this paper, we propose a method to obtain upper bounds for amplitudes of changes of variables in normal form transformations. The criterion is tested on simple mechanical systems with one and two degrees-of-freedom, and for complex as well as real normal form. Its behavior with increasing order in the normal transform is established, and comparisons are drawn between exact solutions and normal form computations for increasing levels of amplitudes. The results clearly establish that the criterion gives an upper bound for validity limit of normal transforms.
Fichier principal
Vignette du fichier
LSIS-INSM_nonli_dyn_2012_thomas.pdf (2.78 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00880968 , version 1 (05-12-2013)

Identifiants

Citer

Claude-Henri Lamarque, Cyril Touzé, Olivier Thomas. An upper bound for validity limits of asymptotic analytical approaches based on normal form theory. Nonlinear Dynamics, 2012, 70 (3), pp.1931-1949. ⟨10.1007/s11071-012-0584-y⟩. ⟨hal-00880968⟩
225 Consultations
340 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More