Research Papers: Gas Turbines: Structures and Dynamics

Nonlinear Modal Analysis of Mistuned Periodic Structures Subjected to Dry Friction

[+] Author and Article Information
C. Joannin

Laboratoire de Tribologie et
Dynamique des Systèmes,
École Centrale de Lyon,
UMR-CNRS 5513,
36 Avenue Guy de Collongue,
Ecully Cedex 69134, France;
Turbomeca—Safran Group,
Bordes Cedex 64511, France
e-mail: colas.joannin@doctorant.ec-lyon.fr

B. Chouvion, F. Thouverez

Laboratoire de Tribologie et
Dynamique des Systèmes,
École Centrale de Lyon,
UMR-CNRS 5513,
36 Avenue Guy de Collongue,
Ecully Cedex 69134, France

M. Mbaye, J.-P. Ousty

Turbomeca—Safran Group,
Bordes Cedex 64511, France

1Corresponding author.

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received September 30, 2015; final manuscript received October 13, 2015; published online December 4, 2015. Editor: David Wisler.

J. Eng. Gas Turbines Power 138(7), 072504 (Dec 04, 2015) (12 pages) Paper No: GTP-15-1468; doi: 10.1115/1.4031886 History: Received September 30, 2015; Revised October 13, 2015

This paper deals with the dynamics of a cyclic system, representative of a bladed disk subjected to dry friction forces, and exhibits structural mistuning. The nonlinear complex modes are computed by solving the eigenproblem associated to the free response of the whole structure and are then used to better understand the forced response to a traveling wave excitation. Similarly to the underlying linear system, the tuned model possesses pairs of modes that can be linearly combined to form traveling waves, unlike those of the mistuned structure. However, due to the nonlinearity, the modal properties are not constant but vary with the vibration amplitude in both cases. A qualitative analysis is also performed to assess the impact of the mistuning magnitude on the response and suggests that further statistical investigations could be of great interest for the design of bladed-disks, in terms of vibration mitigation and robustness.

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Fig. 1

Fundamental sector of the lumped-parameter model with dry friction nonlinearity between the blade root and the disk

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Fig. 2

Traveling wave excitation used to compute the forced response: (a) time series and (b) spatial shape at t/T = 0

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Fig. 3

Regularized friction law governing the nonlinearity ()

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Fig. 4

Influence of the number of retained harmonics on theaccuracy of the solution: (a) relative displacement and (b) amplitude at the tip

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Fig. 5

Forced response and time series of the tuned system for different excitation levelsF

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Fig. 6

Backbone curves (superimposed), time series, and mode shapes at t/T = 0 of the first pair of modes of the tuned system

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Fig. 7

Close-up on the mode shape of mode “a” at t/T = 0 for different amplitude levels

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Fig. 8

Compliance at the blade tips of the tuned system for different excitation levels F

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Fig. 9

Modal damping curves (superimposed) of the first pair of modes of the tuned system as a function of the amplitude of vibration at the blade tips

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Fig. 10

Forced response and time series of blade 2 of the mistuned system for different excitation levels F

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Fig. 11

Backbone curves, time series, and mode shapes at t/T = 0 of the first pair of modes split by the mistuning

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Fig. 12

Compliance at the tip of blade 2 of the mistuned system for different excitation levels F

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Fig. 13

Modal damping curves of the first pair of modes split by the mistuning as a function of the amplitude of vibration of blade 2

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Fig. 14

Response at the tip of another blade of the mistuned system for different excitation levels F

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Fig. 15

Amplification factor between the mistuned and tuned nonlinear systems for F = 2 N

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Fig. 16

Mitigation factor between the nonlinear and underlying linear mistuned systems for F = 2 N



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