Abstract

An investigation of the interaction between Coriolis forces and mistuning on a cyclic symmetric structure is presented in this paper. The sensitivity of the eigenvalues and eigenvectors to mistuning is first studied with the perturbation method. A lumped parameter model is used to perform a modal analysis using a numerical approach after which geometrical nonlinearity is added to compare behavior with the linear case. Two different modes are thoroughly investigated for different rotational speeds, the first with an eigenvalue isolated from the others and the second presenting a frequency veering zone. The evolution from a standing wave domination at low speeds to a traveling wave domination at high speeds is observed for the isolated mode, whereas a standing wave domination remains around the veering zone for the second mode studied. It is also shown that the geometrical nonlinearity reinforces the mistuning effect versus the Coriolis forces.

References

1.
Anderson
,
G.
,
1975
, “
On the Extensional and Flexural Vibrations of Rotating Bars
,”
Int. J. Non-Linear Mech.
,
10
(
5
), pp.
223
236
.10.1016/0020-7462(75)90014-1
2.
Rao
,
J.
,
2011
,
History of Rotating Machinery Dynamics
, Vol.
20
,
Springer Science & Business Media
,
Berlin
.
3.
Subrahmanyam
,
K.
, and
Kaza
,
K.
,
1987
, “
Non-Linear Flap-Lag-Extensional Vibrations of Rotating, Pretwisted, Preconed Beams Including Coriolis Effects
,”
Int. J. Mech. Sci.
,
29
(
1
), pp.
29
43
.10.1016/0020-7403(87)90072-5
4.
Nikolic
,
M.
,
Petrov
,
E. P.
, and
Ewins
,
D. J.
,
2007
, “
Coriolis Forces in Forced Response Analysis of Mistuned Bladed Disks
,”
ASME J. Turbomach.
,
129
(
4
), pp.
730
739
.10.1115/1.2720866
5.
Gibert
,
C.
,
Kharyton
,
V.
,
Thouverez
,
F.
, and
Jean
,
P.
,
2010
, “
On Forced Response of a Rotating Integrally Bladed Disk: Predictions and Experiments
,”
ASME
Paper No. GT2010-23610.10.1115/GT2010-23610
6.
Bucher
,
I.
, and
Ewins
,
D.
,
2001
, “
Modal Analysis and Testing of Rotating Structures
,”
Philos. Trans. R. Soc. London Ser. A
,
359
(
1778
), pp.
61
96
.10.1098/rsta.2000.0714
7.
Wei
,
S.-T.
, and
Pierre
,
C.
,
1988
, “
Localization Phenomena in Mistuned Assemblies With Cyclic Symmetry—Part I: Free Vibrations
,”
ASME J. Vib. Acoust.
,
110
(
4
), pp.
429
438
.10.1115/1.3269547
8.
Wei
,
S.-T.
, and
Pierre
,
C.
,
1988
, “
Localization Phenomena in Mistuned Assemblies With Cyclic Symmetry—Part II: Forced Vibrations
,”
ASME J. Vib. Acoust.
,
110
(
4
), pp.
439
449
.10.1115/1.3269548
9.
Crawley
,
E.
, and
Hall
,
K.
,
1985
, “
Optimization and Mechanisms of Mistuning in Cascades
,”
ASME J. Eng. Gas Turbines Power
,
107
(
2
), pp.
418
426
.10.1115/1.3239742
10.
Nikolic
,
M.
,
2006
, “
New Insights Into the Blade Mistuning Problem
,”
Ph.D. thesis
,
Imperial College London
,
London, UK
.https://www.imperial.ac.uk/media/imperial-college/research-centres-and-groups/dynamics/8295706.PDF
11.
Ruffini
,
V.
,
2016
, “
Coriolis Effects in Bladed Discs
,”
Ph.D. thesis
,
Imperial College London
,
London, UK
.10.25560/61825
12.
Huang
,
B. W.
, and
Kuang
,
J. H.
,
2001
, “
Mode Localization in a Rotating Mistuned Turbo Disk With Coriolis Effect
,”
Int. J. Mech. Sci.
,
43
(
7
), pp.
1643
1660
.10.1016/S0020-7403(00)00096-5
13.
Xin
,
J.
, and
Wang
,
J.
,
2011
, “
Investigation of Coriolis Effect on Vibration Characteristics of a Realistic Mistuned Bladed Disk
,”
ASME
Paper No. GT2011-45453.10.1115/GT2011-45453
14.
Kan
,
X.
, and
Zhao
,
B.
,
2016
, “
Vibration Characteristics of a Mistuned Bladed Disk Considering the Effect of Coriolis Forces
,”
Shock Vib.
,
2016
, pp.
1
9
.10.1155/2016/4656032
15.
Kan
,
X.
, and
Xu
,
Z.
,
2019
, “
Vibration Localization for a Rotating Mistuning Bladed Disk With the Coriolis Effect by a State-Space Decoupling Method
,”
Proc. Inst. Mech. Eng., Part G
,
233
(
3
), pp.
1011
1020
.10.1177/0954410017744238
16.
Kan
,
X.
,
Xu
,
Z.
,
Zhao
,
B.
, and
Zhong
,
J.
,
2017
, “
Effect of Coriolis Force on Forced Response Magnification of Intentionally Mistuned Bladed Disk
,”
J. Sound Vib.
,
399
, pp.
124
136
.10.1016/j.jsv.2017.03.002
17.
Almeida
,
P.
,
Gibert
,
C.
,
Leblanc
,
X.
,
Ousty
,
J.-P.
, and
Thouverez
,
F.
,
2012
, “
Experimental and Numerical Investigations on a Rotating Centrifugal Compressor
,”
ASME
Paper No. GT2012-69760.10.1115/GT2012-69760
18.
Ruffini
,
V.
,
Green
,
J. S.
, and
Schwingshackl
,
C. W.
,
2017
, “
The Influence of Mistuning and Coriolis Effects on the Modal Parameters of Bladed Discs: An Experimental Study
,”
ASME
Paper No. GT2017-63437.10.1115/GT2017-63437
19.
Joannin
,
C.
,
Chouvion
,
B.
,
Thouverez
,
F.
,
Ousty
,
J.-P.
, and
Mbaye
,
M.
,
2017
, “
A Nonlinear Component Mode Synthesis Method for the Computation of Steady-State Vibrations in Non-Conservative Systems
,”
Mech. Syst. Signal Process.
,
83
, pp.
75
92
.10.1016/j.ymssp.2016.05.044
20.
Géradin
,
M.
, and
Rixen
,
D. J.
,
2014
,
Mechanical Vibrations: Theory and Application to Structural Dynamics
,
Wiley
,
Hoboken, NJ
.
21.
Chen
,
S.
,
Yang
,
X.
, and
Lian
,
H.
,
2000
, “
Comparison of Several Eigenvalue Reanalysis Methods for Modified Structures
,”
Struct. Multidiscip. Optim.
,
20
(
4
), pp.
253
259
.10.1007/s001580050155
22.
Sliva
,
G.
,
Brézillon
,
A.
,
Cadou
,
J.-M.
, and
Duigou
,
L.
,
2010
, “
A Study of the Eigenvalue Sensitivity by Homotopy and Perturbation Methods
,”
J. Comput. Appl. Math.
,
234
(
7
), pp.
2297
2302
.10.1016/j.cam.2009.08.086
23.
Gmür
,
T.
,
1997
,
Dynamique Des Structures: Analyse Modale Numérique
,
PPUR Presses Polytechniques
,
Lausanne, Switzerland
.
24.
Powell
,
M. J. D.
,
1968
, “
A FORTRAN Subroutine for Solving Systems of Nonlinear Algebraic Equations
,” Atomic Energy Research Establishment, Harwell, UK, Report No.
AERE-R-5947
.https://www.osti.gov/biblio/4772677-fortran-subroutine-solving-systems-nonlinear-algebraic-equations
25.
Moré
,
J. J.
,
Garbow
,
B. S.
, and
Hillstrom
,
K. E.
,
1980
, “User Guide for MINPACK-1,” Argonne National Laboratory, Argonne, IL, Report No.
ANL-80-74
.10.2172/6997568
26.
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
.10.1115/1.3176036
27.
Nayfeh
,
A. H.
, and
Balachandran
,
B.
,
2008
,
Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods
,
Wiley
,
Hoboken, NJ
.
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