In the structural dynamics design process of turbomachines, Coriolis effects are usually neglected. This assumption holds true if no pronounced interaction between the shaft and disk occurs or if the radial blade displacements are negligible. For classical rotordynamic investigations or for machines where the disk is comparatively thin or weak, Coriolis effects as well as centrifugal effects like stress stiffening and spin softening have to be taken into account. For the analysis of complex structures, the finite element method is today the most commonly used modeling approach. To handle the numerical effort in such an analysis, the aim of the present work is the further development of an existing reduced order model, which also allows the consideration of Coriolis effects without the loss of accuracy for a wide range of rotational speeds. In addition to the investigation of the tuned design of the bladed disk using cyclic boundary conditions, the described method is also appropriate to investigate mistuning phenomena including Coriolis effects. Due to the fact that the computation time can be reduced by two orders of magnitude, the method also opens up the possibility for performing probabilistic mistuning investigations including Coriolis effects.

References

References
1.
Wildheim
,
J.
,
1981
, “
Excitation of Rotating Circumferentially Periodic Structures
,”
J. Sound Vib.
,
75
(
3
), pp.
397
416
.
2.
Jacquet-Richardet
,
G.
,
Ferraris
,
G.
, and
Rieutord
,
P.
,
1996
, “
Frequencies and Modes of Rotating Flexible Bladed Disc-Shaft Assemblies: A Global Cyclic Symmetry Approach
,”
J. Sound Vib.
,
191
(
5
), pp.
901
915
.
3.
Sternschüss
,
A.
, and
Balmès
,
E.
,
2006
, “
On the Reduction of Quasi-Cyclic Disk Models With Variable Rotation Speeds
,” ISMA, pp. 3925–3939.
4.
Yang
,
M.-T.
, and
Griffin
,
J. H.
,
2001
, “
A Reduced-Order Model of Mistuning Using a Subset of Nominal System Modes
,”
ASME J. Eng. Gas Turbines Power
,
123
(
4
), pp.
893
900
.
5.
Marugabandhu
,
P.
, and
Griffin
,
J. H.
,
2003
, “
A Reduced-Order Model for Evaluating the Effect of Rotational Speed on the Natural Frequencies and Mode Shapes of Blades
,”
ASME J. Eng. Gas Turbines Power
,
125
(
3
), pp.
772
776
.
6.
Mlejnek
,
H. P.
, and
Schreieck
,
R.
,
1976
, “
Einsatz Der Finite Elemente Methode Zur Statischen Und Dynamischen Berechnung Von Schalenartigen Radial- Und Axialschaufeln Bei Beliebigen Drehzahlen (System Turban)
,”
VDI-Berichte Nr
,.
264
, pp.
173
178
.
7.
Bossak
,
M. A. J.
, and
Zienkiewicz
,
O. C.
,
1973
, “
Free Vibration of Initially Stressed Solids, With Particular Reference to Centrifugalforce Effects in Rotating Machinery
,”
J. Strain Anal. Eng. Des.
,
8
(4), pp.
245
252
.
8.
Bucher
,
I.
, and
Ewins
,
D. J.
,
2001
, “
Modal Analysis and Testing of Rotating Structures
,”
Philos. Trans. R. Soc. A
,
359
(
1778
), pp.
61
96
.
9.
Ewins
,
D. J.
,
2000
,
Modal Testing: Theory, Practice and Application
,
2nd ed.
,
Research Studies Press
,
Baldock, UK
.
10.
Mead
,
D. J.
,
1973
, “
A General Theory of Harmonic Wave Propagation in Linear Periodic Systems With Multiple Coupling
,”
J. Sound Vib.
,
27
(
2
), pp.
235
260
.
11.
Thomas
,
D. L.
,
1979
, “
Dynamics of Rotationally Periodic Structures
,”
Int. J. Numer. Methods Eng.
,
14
(
1
), pp.
81
102
.
12.
Meirovitch
,
L.
, and
Ryland
,
G.
, II
,
1979
, “
Response of Slightly Damped Gyroscopic Systems
,”
J. Sound Vib.
,
67
(
1
), pp.
1
19
.
13.
Allemang
,
R. J.
, and
Brown
,
D. L.
,
1982
, “
A Correlation Coefficient for Modal Vector Analysis
,”
First International Modal Analysis Conference & Exhibit
, pp.
110
116
.
14.
Bladh
,
R.
,
Pierre
,
C.
,
Castanier
,
M. P.
, and
Kruse
,
M. J.
,
2002
, “
Dynamic Response Predictions for a Mistuned Industrial Turbomachinery Rotor Using Reduced-Order Modeling
,”
ASME J. Eng. Gas Turbines Power
,
124
(
2
), pp.
311
324
.
15.
Baron Rayleigh
,
J. W. S.
,
1894
,
The Theory of Sound
, Vol.
1
,
Macmillan and Co
,
Cambridge, UK
.
16.
Myhre
,
M.
,
Moyroud
,
F.
, and
Fransson
,
T. H.
,
2003
, “
Numerical Investigation of the Sensitivity of Forced Response Characteristics of Bladed Disks to Mistuning
,”
ASME
Paper No. GT2003-38007
.
17.
Hoppe
,
R.
,
1871
, “
The Bending Vibration of a Circular Ring
,”
Crelle. J. Math.
,
73
(
73
), p.
158
.
18.
Bryan
,
G. H.
,
1890
, “
On the Beats in the Vibrations of a Revolving Cylinder of Shell
,”
Proc. Cambridge Philos. Soc.
,
7
, pp.
101
111
.
19.
Endo
,
M.
,
Hatamura
,
K.
,
Sakato
,
M.
, and
Taniguchi
,
O.
,
1984
, “
Flexural Vibration of a Thin Rotating Ring
,”
J. Sound Vib.
,
92
(
2
), pp.
261
272
.
20.
Genta
,
G.
, and
Silvagni
,
M.
,
2014
, “
On Centrifugal Softening in Finite Element Method Rotordynamics
,”
ASME J. Appl. Mech.
,
81
(
1
), p.
011001
.
21.
Kan
,
X.
, and
Zhao
,
B.
,
2016
, “
Vibration Characteristics of a Mistuned Bladed Disk Considering the Effect of Coriolis Forces
,”
Shock Vib.
,
2016
, p. 4656032.
22.
Castanier
,
M. P.
, and
Pierre
,
C.
,
2006
, “
Modeling and Analysis of Mistuned Bladed Disk Vibration: Status and Emerging Directions
,”
J. Propul. Power
,
22
(
2
), pp.
384
396
.
23.
Mai
,
M.-M.
,
1985
, “
Zur Nichtlinear Statischen Und Dynamischen Berechnung Gyroskopischer Schalen- Und Balkenstrukturen Mit Der Finite Element Methode
,” Ph. D. dissertation, Universität Stuttgart, Stuttgart, Germany.
24.
Southwell
,
R. V.
,
1922
, “
On the Free Transverse Vibrations of a Uniform Circular Disc Clamped at Its Centre; and on the Effects of Rotation
,”
Proc. R. Soc. Lond. A
,
101
(
709
), pp.
133
153
.
25.
du Bois
,
J. L.
,
Adhikari
,
S.
, and
Lieven
,
N. A. J.
,
2011
, “
On the Quantification of Eigenvalue Curve Veering: A Veering Index
,”
ASME J. Appl. Mech.
,
78
(
4
), p.
041007
.
26.
Ruffini
,
V.
,
Schwingshackl
,
C. W.
, and
Green
,
J. S.
,
2015
, “
Prediction Capabilities of Coriolis and Gyroscopic Effects in Current Finite Element Software
,”
Ninth IFToMM International Conference on Rotor Dynamics
, Milan, Italy, Sept. 22–25, pp.
1853
1862
.
27.
Kruse
,
M.
, and
Pierre
,
C.
,
1996
, “
Dynamic Response of an Industrial Turbomachinery Rotor
,”
AIAA
Paper No. AIAA-96-2820
.
28.
Whitehead
,
D. S.
,
1966
, “
Effect of Mistuning on the Vibration of Turbomachine Blades Induced by Wakes
,”
Proc. Inst. Mech. Eng. C
,
8
(
1
), pp.
15
21
.
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