This work is devoted to the study of non linear dynamics of structures with cyclic symmetry under geometrical nonlinearity using the harmonic balance method (HBM). In order to study the influence of the non-linearity 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, a 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. The 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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ASME Turbo Expo 2010: Power for Land, Sea, and Air
June 14–18, 2010
Glasgow, UK
Conference Sponsors:
- International Gas Turbine Institute
ISBN:
978-0-7918-4401-4
PROCEEDINGS PAPER
Vibration Analysis of a Nonlinear System With Cyclic Symmetry Available to Purchase
Aure´lien Grolet,
Aure´lien Grolet
E´cole Centrale de Lyon, Ecully, France
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Fabrice Thouverez
Fabrice Thouverez
E´cole Centrale de Lyon, Ecully, France
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Aure´lien Grolet
E´cole Centrale de Lyon, Ecully, France
Fabrice Thouverez
E´cole Centrale de Lyon, Ecully, France
Paper No:
GT2010-22681, pp. 917-929; 13 pages
Published Online:
December 22, 2010
Citation
Grolet, A, & Thouverez, F. "Vibration Analysis of a Nonlinear System With Cyclic Symmetry." Proceedings of the ASME Turbo Expo 2010: Power for Land, Sea, and Air. Volume 6: Structures and Dynamics, Parts A and B. Glasgow, UK. June 14–18, 2010. pp. 917-929. ASME. https://doi.org/10.1115/GT2010-22681
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