Vibration analysis of a nonlinear system with cyclic symmetry / Aurélien Grolet in Transactions of the ASME . Journal of engineering for gas turbines and power, Vol. 133 N° 2 (Fevrier 2011)  

Public ISBD [article]  inTransactions of the ASME . Journal of engineering for gas turbines and power > Vol. 133 N° 2 (Fevrier 2011) . - 09 p. Titre : Vibration analysis of a nonlinear system with cyclic symmetry Type de document : texte imprimé Auteurs : Aurélien Grolet, Auteur ; Fabrice Thouverez, Auteur Année de publication : 2012 Article en page(s) : 09 p. Note générale : Génie Mécanique Langues : Anglais (eng) Mots-clés : Bifurcation Dynamic response Nonlinear differential equations systems Stability Index. décimale : 620.1 Essais des matériaux. Défauts des matériaux. Protection des matériaux Résumé : This work is devoted to the study of nonlinear dynamics of structures with cyclic symmetry under geometrical nonlinearity using the harmonic balance method (HBM). In order to study the influence of the nonlinearity due to large deflection of blades, a simplified model has been developed. It leads to nonlinear differential equations of the second order, linearly coupled, in which the nonlinearity appears by cubic terms. Periodic solutions in both free and forced cases are sought by the HBM coupled with an arc length continuation and stability analysis. In this study, specific attention has been paid to the evaluation of nonlinear modes and to the influence of excitation on dynamic responses. Indeed, several cases of excitation have been analyzed: punctual one and tuned or detuned low engine order. This paper shows that for a localized, or sufficiently detuned, excitation, several solutions can coexist, some of them being represented by closed curves in the frequency-amplitude domain. Those different kinds of solution meet up when increasing the force amplitude, leading to forced nonlinear localization. As the closed curves are not tied with the basic nonlinear solution, they are easily missed. They were calculated using a sequential continuation with the force amplitude as a parameter. DEWEY : 620.1 ISSN : 0742-4795 En ligne : http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JETPEZ00013 [...] [article] Vibration analysis of a nonlinear system with cyclic symmetry [texte imprimé] / Aurélien Grolet, Auteur ; Fabrice Thouverez, Auteur . - 2012 . - 09 p. Génie Mécanique Langues : Anglais (eng) in Transactions of the ASME . Journal of engineering for gas turbines and power > Vol. 133 N° 2 (Fevrier 2011) . - 09 p. Mots-clés : Bifurcation Dynamic response Nonlinear differential equations systems Stability Index. décimale : 620.1 Essais des matériaux. Défauts des matériaux. Protection des matériaux Résumé : This work is devoted to the study of nonlinear dynamics of structures with cyclic symmetry under geometrical nonlinearity using the harmonic balance method (HBM). In order to study the influence of the nonlinearity due to large deflection of blades, a simplified model has been developed. It leads to nonlinear differential equations of the second order, linearly coupled, in which the nonlinearity appears by cubic terms. Periodic solutions in both free and forced cases are sought by the HBM coupled with an arc length continuation and stability analysis. In this study, specific attention has been paid to the evaluation of nonlinear modes and to the influence of excitation on dynamic responses. Indeed, several cases of excitation have been analyzed: punctual one and tuned or detuned low engine order. This paper shows that for a localized, or sufficiently detuned, excitation, several solutions can coexist, some of them being represented by closed curves in the frequency-amplitude domain. Those different kinds of solution meet up when increasing the force amplitude, leading to forced nonlinear localization. As the closed curves are not tied with the basic nonlinear solution, they are easily missed. They were calculated using a sequential continuation with the force amplitude as a parameter. DEWEY : 620.1 ISSN : 0742-4795 En ligne : http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JETPEZ00013 [...]

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