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.
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February 2011
Research Papers
Vibration Analysis of a Nonlinear System With Cyclic Symmetry
Aurélien Grolet,
Aurélien Grolet
Laboratoire de Tribologie et Dynamique des Systèmes 36,
e-mail: aurelien.grolet@ecl2009.ec-lyon.fr
École Centrale de Lyon
, Avenue Guy de Collongue, 69134 Ecully Cedex, France
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Fabrice Thouverez
Fabrice Thouverez
Laboratoire de Tribologie et Dynamique des Systèmes 36,
École Centrale de Lyon
, Avenue Guy de Collongue, 69134 Ecully Cedex, France
Search for other works by this author on:
Aurélien Grolet
Laboratoire de Tribologie et Dynamique des Systèmes 36,
École Centrale de Lyon
, Avenue Guy de Collongue, 69134 Ecully Cedex, Francee-mail: aurelien.grolet@ecl2009.ec-lyon.fr
Fabrice Thouverez
Laboratoire de Tribologie et Dynamique des Systèmes 36,
École Centrale de Lyon
, Avenue Guy de Collongue, 69134 Ecully Cedex, FranceJ. Eng. Gas Turbines Power. Feb 2011, 133(2): 022502 (9 pages)
Published Online: October 26, 2010
Article history
Received:
April 12, 2010
Revised:
April 26, 2010
Online:
October 26, 2010
Published:
October 26, 2010
Citation
Grolet, A., and Thouverez, F. (October 26, 2010). "Vibration Analysis of a Nonlinear System With Cyclic Symmetry." ASME. J. Eng. Gas Turbines Power. February 2011; 133(2): 022502. https://doi.org/10.1115/1.4001989
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