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Research Papers

Dynamic Analysis and Reduction of a Cyclic Symmetric System Subjected to Geometric Nonlinearities

[+] Author and Article Information
Adrien Martin

Laboratoire de Tribologie et
Dynamique des Systèmes,
École Centrale de Lyon,
Écully CEDEX 69134, France
e-mail: adrien.martin@doctorant.ec-lyon.fr

Fabrice Thouverez

Laboratoire de Tribologie et
Dynamique des Systèmes,
École Centrale de Lyon,
Écully CEDEX 69134, France

1Corresponding author.

Manuscript received June 25, 2018; final manuscript received June 29, 2018; published online December 5, 2018. Editor: Jerzy T. Sawicki.

J. Eng. Gas Turbines Power 141(4), 041027 (Dec 05, 2018) (8 pages) Paper No: GTP-18-1335; doi: 10.1115/1.4041001 History: Received June 25, 2018; Revised June 29, 2018

The search for ever lighter weight has become a major goal in the aeronautical industry as it has a direct impact on fuel consumption. It also implies the design of increasingly thin structures made of sophisticated and flexible materials. This may result in nonlinear behaviors due to large structural displacements. Stator vanes can be affected by such phenomena, and as they are a critical part of turbojets, it is crucial to predict these behaviors during the design process in order to eliminate them. This paper presents a reduced order modeling process suited for the study of geometric nonlinearities. The method is derived from a classical component mode synthesis (CMS) with fixed interfaces, in which the reduced nonlinear terms are obtained through a stiffness evaluation procedure (STEP) procedure using an adapted basis composed of linear modes completed by modal derivatives (MD). The whole system is solved using a harmonic balance procedure and a classic iterative nonlinear solver. The application is implemented on a schematic stator vane model composed of nonlinear Euler–Bernoulli beams under von Kàrmàn assumptions.

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Figures

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Fig. 1

Harmonic balance method procedure of the reduced system

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Fig. 2

Stator vane model: (a) cyclic symmetric model, (b) beam representation, (c) dimensions of the reference sector, and (d) FE representation of the reference sector

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Fig. 3

Mode shapes of the first flexural mode family: (a) 3 diameters, (b) 2 diameters, (c) 1 diameter, and (d) 0 diameter

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Fig. 4

Linear forced response of the system for F = 1 N

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Fig. 5

Comparison of the results obtained with reduction on beam 1

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Fig. 6

Comparison of the results obtained with 3 and 5 harmonics in the HBM on the beam 1 with F = 1.1 N

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Fig. 7

Pulsation-energy diagram of the full nonlinear system for several forcing amplitudes (linear: - -, nonlinear: 0.1N, 0.3N, 0.6N, 0.8N, 1.1N)

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Fig. 8

Highlighting the localization on the 1 diameter mode for F = 1.1 N: (a) forced responses associated with the frequency range of interest, (b) nonlinear time evolution of the transversal DOF at the middle of each beam (•), and (c) linear time evolution of the transversal DOF at the middle of each beam (•)

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Fig. 9

Comparison of the full and reduced models: (a) forced responses of the system, (b) nonlinear time evolution of the transversal DOF at the middle of each beam: full nonlinear system F = 0.6 N, and (c) nonlinear time evolution of the transversal DOF at the middle of each beam: reduced nonlinear system F = 0.6 N

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Fig. 10

Influence of the thickness of the rings (linear: - -, nonlinear: 0.1N, 0.5N, 0.8N, 1.1N): (a) tc = 0.6 cm, (b) tc = 0.6 cm, (c) tc = 0.8 cm, (d) tc = 0.8 cm, (e) tc = 1.2 cm, (f) tc = 1.2 cm, (g) tc = 1.4 cm, and (h) tc = 1.4 cm

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