0
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.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Petrov, E. , and Ewins, D. , 2006, “ Effects of Damping and Varying Contact Area at Bladed-Disk Joints in Forced Responses Analysis of Bladed Disk Assemblies,” ASME J Turbomach., 128(2), pp. 403–410. [CrossRef]
Laxalde, D. , Thouverez, F. , Sinou, J.-J. , and Lombard, J.-P. , 2007, “ Qualitative Analysis of Forced Response of Blisks With Friction Ring Dampers,” Eur. J. Mech.-A/Solids, 26(4), pp. 676–687. [CrossRef]
Salles, L. , Blanc, L. , Thouverez, F. , and Gouskov, A. , 2011, “ Dynamic Analysis of Fretting-Wear in Friction Contact Interfaces,” Int. J. Solids Struct., 48(10), pp. 1513–1524. [CrossRef]
Nacivet, S. , Pierre, C. , Thouverez, F. , and Jezequel, L. , 2003, “ A Dynamic Lagrangian Frequency–Time Method for the Vibration of Dry-Friction-Damped Systems,” J. Sound Vib., 265(1), pp. 201–219. [CrossRef]
Charleux, D. , Gibert, C. , Thouverez, F. , and Dupeux, J. , 2006, “ Numerical and Experimental Study of Friction Damping in Blade Attachments of Rotating Bladed Disks,” Int. J. Rotating Mach., 2006, p. 71302. [CrossRef]
Berruti, T. , Firrone, C. , and Gola, M. , 2011, “ A Test Rig for Noncontact Traveling Wave Excitation of a Bladed Disk With Underplatform Dampers,” ASME J. Eng. Gas Turbines Power, 133(3), p. 032502. [CrossRef]
Zucca, S. , Maio, D. D. , and Ewins, D. , 2012, “ Measuring the Performance of Underplatform Dampers for Turbine Blades by Rotating Laser Doppler Vibrometer,” Mech. Syst. Signal Process., 32, pp. 269–281. [CrossRef]
Schwingshackl, C. , Petrov, E. , and Ewins, D. , 2012, “ Measured and Estimated Friction Interface Parameters in a Nonlinear Dynamic Analysis,” Mech. Syst. Signal Process., 28, pp. 574–584. [CrossRef]
Schwingshackl, C. , Joannin, C. , Pesaresi, L. , Green, J. , and Hoffmann, N. , 2014, “ Test Method Development for Nonlinear Damping Extraction of Dovetail Joints,” Dynamics of Coupled Structures, Vol. 1, Springer, Cham, Switzerland, pp. 229–237.
Pierre, C. , and Dowell, E. , 1987, “ Localization of Vibrations by Structural Irregularity,” J. Sound Vib., 114(3), pp. 549–564. [CrossRef]
Castanier, M. P. , and Pierre, C. , 2002, “ Using Intentional Mistuning in the Design of Turbomachinery Rotors,” AIAA J., 40(10), pp. 2077–2086. [CrossRef]
Mbaye, M. , Soize, C. , Ousty, J.-P. , and Capiez-Lernout, E. , 2013, “ Robust Analysis of Design in Vibration of Turbomachines,” ASME J. Turbomach., 135, p. 021008. [CrossRef]
Pichot, F. , Laxalde, D. , Sinou, J.-J. , Thouverez, F. , and Lombard, J.-P. , 2006, “ Mistuning Identification for Industrial Blisks Based on the Best Achievable Eigenvector,” Comput. Struct., 84(29–30), pp. 2033–2049. [CrossRef]
Vargiu, P. , Firrone, C. , Zucca, S. , and Gola, M. , 2011, “ A Reduced Order Model Based on Sector Mistuning for the Dynamic Analysis of Mistuned Bladed Disks,” Int. J. Mech. Sci., 53(8), pp. 639–646. [CrossRef]
Ewins, D. , 2000, Modal Testing: Theory Practice and Application, 2nd ed., Research Study Press, Baldock, UK.
Rosenberg, R. , 1962, “ The Normal Modes of Nonlinear n-Degrees-of-Freedom Systems,” ASME J. Appl. Mech., 29(1), pp. 1–74. [CrossRef]
Kerschen, G. , Peeters, M. , Golinval, J. , and Vakakis, A. , 2009, “ Nonlinear Normal Modes—Part I: A Useful Framework for the Structural Dynamicist,” Mech. Syst. Signal Process., 23(1), pp. 170–194. [CrossRef]
Shaw, S. , and Pierre, C. , 1993, “ Normal Modes for Non-Linear Vibratory Systems,” J. Sound Vib., 164(1), pp. 85–124. [CrossRef]
Vakakis, A. F. , 1992, “ Dynamics of a Nonlinear Periodic Structure With Cyclic Symmetry,” Acta Mech., 95(1–4), pp. 197–226. [CrossRef]
Vakakis, A. F. , and Cetinkaya, C. , 1993, “ Mode Localization in a Class of Multidegree-of-Freedom Nonlinear Systems With Cyclic Symmetry,” SIAM J. Appl. Math., 53(1), pp. 265–282. [CrossRef]
Vakakis, A. , Nayfeh, T. , and King, M. , 1993, “ A Multiple-Scales Analysis of Nonlinear, Localized Modes in a Cyclic Periodic System,” ASME J. Appl. Mech., 60(2), pp. 388–397. [CrossRef]
Laxalde, D. , and Thouverez, F. , 2009, “ Complex Non-Linear Modal Analysis for Mechanical Systems: Application to Turbomachinery Bladings With Friction Interfaces,” J. Sound Vib., 322(4–5), pp. 1009–1025. [CrossRef]
Krack, M. , von Scheidt, L. P. , and Wallaschek, J. , 2013, “ A Method for Nonlinear Modal Analysis and Synthesis: Application to Harmonically Forced and Self-Excited Mechanical Systems,” J. Sound Vib., 332(25), pp. 6798–6814. [CrossRef]
Wei, S.-T. , and Pierre, C. , 1989, “ Effects of Dry Friction Damping on the Occurrence of Localized Forced Vibrations in Nearly Cyclic Structures,” J. Sound Vib., 129(3), pp. 397–416. [CrossRef]
Grolet, A. , and Thouverez, F. , 2012, “ Free and Forced Vibration Analysis of a Nonlinear System With Cyclic Symmetry: Application to a Simplified Model,” J. Sound Vib., 331(12), pp. 2911–2928. [CrossRef]
Cameron, T. M. , and Griffin, J. H. , 1989, “ An Alternating Frequency/Time Domain Method for Calculating the Steady-State Response of Nonlinear Dynamic Systems,” ASME J. Appl. Mech., 56(1), pp. 149–154. [CrossRef]
Nayfeh, A. , and Balachandran, B. , 1995, Applied Nonlinear Dynamics: Analytical, Computational and Experimental Methods, Wiley-VCH Verlag, Weinheim, Germany.
Petrov, E. , and Ewins, D. , 2003, “ Analytical Formulation of Friction Interface Elements for Analysis of Nonlinear Multi-Harmonic Vibrations of Bladed Disks,” ASME J. Turbomach., 125(2), pp. 364–371. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

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

Grahic Jump Location
Fig. 2

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

Grahic Jump Location
Fig. 3

Regularized friction law governing the nonlinearity ()

Grahic Jump Location
Fig. 4

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

Grahic Jump Location
Fig. 5

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

Grahic Jump Location
Fig. 6

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

Grahic Jump Location
Fig. 7

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

Grahic Jump Location
Fig. 8

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

Grahic Jump Location
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

Grahic Jump Location
Fig. 10

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

Grahic Jump Location
Fig. 11

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

Grahic Jump Location
Fig. 12

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

Grahic Jump Location
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

Grahic Jump Location
Fig. 14

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

Grahic Jump Location
Fig. 15

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

Grahic Jump Location
Fig. 16

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

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In