Nonlinear analysis, instability and routes to chaos of a cracked rotating shaft
TypeArticles dans des revues avec comité de lecture
The aim of this paper is to explore the dynamical response of a rotating shaft with a cracked transverse section. This complex problem is distilled down to the study of a very comprehensive mechanical system composed of two non-cracked rigid bars connected with a nonlinear bending spring that concentrates the global stiffness of the cracked shaft. The switching crack model is presented as a specific case of the EDF-LMS family of models and adopted to describe the breathing mechanism of the crack. By analyzing the system equilibrium equations, we show that the stiffness change when the crack breathes leads to shocks with velocity jumps and coupling between the transverse oscillations. The linear stability of the periodic solutions is examined based on the Floquet’s theory. Nonlinear dynamics tools such as Poincaré maps and bifurcation diagrams are used to unveil the system oscillations characteristics. Many well-known features due to the crack presence have been observed, but some unexpected responses are noticed like chaotic behavior. This can be confidently attributed to the abrupt change of the structure stiffness with the breathing crack. It has also been observed that with the super-harmonic resonance phenomenon, the increase of static deflection accompanied by that of the first two harmonics amplitudes are good indicators of a propagating crack presence.
Fichier(s) constituant cette publication
Cette publication figure dans le(s) laboratoire(s) suivant(s)
Visualiser des documents liés par titre, auteur, créateur et sujet.
NASRI, Mohamed Aziz; AGUADO, Jose Vicente; AMMAR, Amine; CUETO, Elias; CHINESTA, Francisco; MOREL, Franck; ROBERT, Camille; EL AREM, Saber (Key Engineering Materials, 2015)Forming processes usually involve irreversible plastic transformations. The calculation in that case becomes cumbersome when large parts and processes are considered. Recently Model Order Reduction techniques opened new ...
Proper Generalized Decomposition (PGD) for numerical calculation of polycrystalline aggregates under cyclic loading NASRI, Mohamed Aziz; ROBERT, Camille; EL AREM, Saber; MOREL, Franck; AMMAR, Amine (2015)none
NASRI, Mohamed Aziz; AMMAR, Amine; CHINESTA, Francisco; ROBERT, Camille; EL AREM, Saber; MOREL, Franck (Springer, 2016)Forming processes usually involve irreversible plastic transformations. The calculation in that case becomes cumbersome when large parts and processes are considered. Recently Model Order Reduction techniques ...
EL AREM, Saber; NGUYEN, Quoc Son (Springer, 2012)In this paper, the effects of a breathing crack on the vibratory characteris- tics of a rotating shaft are investigated. A new, simple and robust model composed of two rigid bars connected with a nonlinear flexural spring ...
Réduction dimensionnelle de type PGD pour le calcul numérique d’agrégats polycristallin soumis à des chargements cycliques NASRI, Mohamed Aziz; ROBERT, Camille; MOREL, Franck; EL AREM, Saber; AMMAR, Amine (AFM, 2015)Les modélisations numériques des matériaux à l’échelle de la microstructure se sont fortement développées au cours des deux dernières décennies. Malheureusement, les méthodes de résolution classiques ne permettent pas de ...