Abstract

A new operational modal analysis (OMA) method is developed for estimation of modal parameters (MPs) of a rotating structure (RS) subject to random excitation using a nonuniform rotating beam model, an image processing method, and an improved demodulation method. The solution to the governing equation of a nonuniform rotating beam is derived, which can be considered as the response of the beam measured by a continuously scanning laser Doppler vibrometer (CSLDV) system. A recently developed tracking CSLDV system can track and scan the RS. The image processing method determines the angular position of the RS so that the tracking CSLDV system can sweep its laser spot along a time-varying path on it. The improved demodulation method obtains undamped mode shapes (UMSs) of the RS by multiplying its measured response by sinusoids whose frequencies are its damped natural frequencies (DNFs) that are obtained from the fast Fourier transform (FFT) of the measured response. Experimental investigation of the OMA method using the tracking CSLDV system is conducted, and MPs of a rotating fan blade (RFB), including DNFs and UMSs, with different constant speeds and its instantaneous MPs with a nonconstant speed are estimated. Estimated first DNFs and UMSs of the stationary fan blade and RFB are compared with those from the lifting method that was previously developed by the authors.

References

1.
Bell
,
J. R.
, and
Rothberg
,
S. J.
,
2000
, “
Laser Vibrometers and Contacting Transducers, Target Rotation and Six Degree-of-Freedom Vibration: What Do We Really Measure?
,”
J. Sound Vib.
,
237
(
2
), pp.
245
261
.
2.
Rothberg
,
S.
,
Allen
,
M.
,
Castellini
,
P.
,
Di Maio
,
D.
,
Dirckx
,
J. J. J.
,
Ewins
,
D. J.
,
Halkon
,
B. J.
,
Muyshondt
,
P.
,
Paone
,
N.
,
Ryan
,
T.
,
Steger
,
H.
,
Tomasini
,
E. P.
,
Vanlanduit
,
S.
, and
Vignola
,
J. F.
,
2017
, “
An International Review of Laser Doppler Vibrometry: Making Light Work of Vibration Measurement
,”
Opt. Lasers Eng.
,
99
(
1
), pp.
11
22
.
3.
Sriram
,
P.
,
Hanagud
,
S.
,
Craig
,
J.
, and
Komerath
,
N. M.
,
1990
, “
Scanning Laser Doppler Technique for Velocity Profile Sensing on a Moving Surface
,”
Appl. Opt.
,
29
(
16
), pp.
2409
2417
.
4.
Sriram
,
P.
,
Hanagud
,
S.
, and
Craig
,
J.
,
1992
, “
Mode Shape Measurement Using a Scanning Laser Doppler Vibrometer
,”
Int. J. Anal. Exp. Modal Anal.
,
7
(
3
), pp.
169
178
.
5.
Allen
,
M. S.
, and
Sracic
,
M. W.
,
2010
, “
A New Method for Processing Impact Excited Continuous-Scan Laser Doppler Vibrometer Measurements
,”
Mech. Syst. Signal Process
,
24
(
3
), pp.
721
735
.
6.
Chen
,
D. M.
,
Xu
,
Y. F.
, and
Zhu
,
W. D.
,
2016
, “
Damage Identification of Beams Using a Continuously Scanning Laser Doppler Vibrometer System
,”
ASME J. Vib. Acoust.
,
138
(
5
), p.
051011
.
7.
Stanbridge
,
A.
, and
Ewins
,
D.
,
1996
, “
Using a Continuously-Scanning Laser Doppler Vibrometer for Modal Testing
,”
14th International Modal Analysis Conference (IMAC)
,
Dearborn, MI
,
Feb. 12–15
, pp.
816
822
.
8.
Stanbridge
,
A.
, and
Ewins
,
D.
,
1999
, “
Modal Testing Using a Scanning Laser Doppler Vibrometer
,”
Mech. Syst. Signal Process
,
13
(
2
), pp.
255
270
.
9.
Stanbridge
,
A.
,
Ewins
,
D.
, and
Khan
,
A.
,
2000
, “
Modal Testing Using Impact Excitation and a Scanning LDV
,”
Shock Vib.
,
7
(
2
), pp.
91
100
.
10.
Di Maio
,
D.
, and
Ewins
,
D.
,
2011
, “
Continuous Scan, a Method for Performing Modal Testing Using Meaningful Measurement Parameters; Part I
,”
Mech. Syst. Signal Process
,
25
(
8
), pp.
3027
3042
.
11.
Chen
,
D. M.
,
Xu
,
Y. F.
, and
Zhu
,
W. D.
,
2017
, “
Experimental Investigation of Notch-Type Damage Identification With a Curvature-Based Method by Using a Continuously Scanning Laser Doppler Vibrometer System
,”
J. Nondestr. Eval.
,
36
(
2
), p.
38
.
12.
Chen
,
D. M.
,
Xu
,
Y. F.
, and
Zhu
,
W. D.
,
2018
, “
Identification of Damage in Plates Using Full-Field Measurement With a Continuously Scanning Laser Doppler Vibrometer System
,”
J. Sound Vib.
,
422
(
5
), pp.
542
567
.
13.
Xu
,
Y. F.
,
Chen
,
D. M.
, and
Zhu
,
W. D.
,
2017
, “
Damage Identification of Beam Structures Using Free Response Shapes Obtained by Use of a Continuously Scanning Laser Doppler Vibrometer System
,”
Mech. Syst. Signal Process
,
92
(
8
), pp.
226
247
.
14.
Xu
,
Y. F.
,
Chen
,
D. M.
, and
Zhu
,
W. D.
,
2020
, “
Modal Parameter Estimation Using Free Response Measured by a Continuously Scanning Laser Doppler Vibrometer System With Application to Structural Damage Identification
,”
J. Sound Vib.
,
485
(
10
), p.
115536
.
15.
Yuan
,
K.
, and
Zhu
,
W. D.
,
2021
, “
Estimation of Modal Parameters of a Beam Under Random Excitation Using a Novel 3D Continuously Scanning Laser Doppler Vibrometer System And an Extended Demodulation Method
,”
Mech. Syst. Signal Process
,
155
(
6
), p.
107606
.
16.
Yang
,
S.
, and
Allen
,
M. S.
,
2012
, “
Output-Only Modal Analysis Using Continuous-Scan Laser Doppler Vibrometry and Application to a 20kw Wind Turbine
,”
Mech. Syst. Signal Process
,
31
(
8
), pp.
228
245
.
17.
Wereley
,
N. M.
, and
Hall
,
S. R.
,
1990
, “
Frequency Response
of
Linear Time Periodic Systems
,”
29th IEEE Conference on Decision and Control
,
Honolulu, HI
,
Dec. 5–7
, pp.
3650
3655
.
18.
Yang
,
S.
, and
Allen
,
M. S.
,
2014
, “
Lifting Approach to Simplify Output-Only Continuous-Scan Laser Vibrometry
,”
Mech. Syst. Signal Process
,
45
(
2
), pp.
267
282
.
19.
Xu
,
Y. F.
,
Chen
,
D. M.
, and
Zhu
,
W. D.
,
2019
, “
Operational Modal Analysis Using Lifted Continuously Scanning Laser Doppler Vibrometer Measurements and Its Application to Baseline-Free Structural Damage Identification
,”
J. Vib. Control
,
25
(
7
), pp.
1341
1364
.
20.
Stanbridge
,
A. B.
,
Martarelli
,
M.
, and
Ewins
,
D. J.
,
2001
, “
Rotating Disc Vibration Analysis With a Circular-Scanning LDV
,”
Proceedings of SPIE, the International Society for Optical Engineering
,
Orlando, FL
,
Feb. 5–8
, pp.
464
469
.
21.
Bucher
,
I.
,
Schmiechen
,
P.
,
Robb
,
D. A.
, and
Ewins
,
D. J.
,
1994
, “
Laser-Based Measurement System for Measuring the Vibration on Rotating Discs
,”
First International Conference on Vibration Measurements by Laser Techniques: Advances and Applications
,
Ancona, Italy
,
Oct. 3–5
, pp.
398
408
.
22.
Castellini
,
P.
,
Giovanucci
,
F.
,
Nava-Mambretti
,
G.
,
Scalise
,
L.
, and
Tomasini
,
E. P.
,
1998
, “
Vibration Analysis
of
Tyre Treads: A In-Plane Laser Vibrometry Approach
,”
16th International Modal Analysis Conference
,
Santa Barbara, CA
,
Feb. 2–5
, Society for Experimental Mechanics, Inc., Vol.
2
, pp.
1732
1738
.
23.
Fioretti
,
A.
,
Di Maio
,
D.
,
Ewins
,
D. J.
,
Castellini
,
P.
, and
Tomasini
,
E. P.
,
2010
, “
Deflection Shape Reconstructions of a Rotating Five-Blade Helicopter Rotor From TLDV Measurements
,”
AIP Conf. Proc.
,
1253
(
1
), pp.
17
28
.
24.
Di Maio
,
D.
, and
Ewins
,
D. J.
,
2010
, “
Applications of Continuous Tracking SLDV Measurement Methods to Axially Symmetric Rotating Structures Using Different Excitation Methods
,”
Mech. Syst. Signal Process
,
24
(
8
), pp.
3013
3036
.
25.
Gasparoni
,
A.
,
Allen
,
M. S.
,
Yang
,
S.
,
Sracic
,
M. W.
,
Castellini
,
P.
, and
Tomasini
,
E. P.
,
2010
, “
Experimental Modal Analysis on a Rotating Fan Using Tracking-CSLDV
,”
AIP Conf. Proc.
,
1253
(
1
), pp.
3
16
.
26.
Martarelli
,
M.
,
Castellini
,
P.
,
Santolini
,
C.
, and
Tomasini
,
E. P.
,
2011
, “
Laser Doppler Vibrometry on Rotating Structures in Coast-Down: Resonance Frequencies and Operational Deflection Shape Characterization
,”
Meas. Sci. Technol.
,
22
(
11
), p.
115106
.
27.
Khalil
,
H.
,
Kim
,
D.
,
Nam
,
J.
, and
Park
,
K.
,
2015
, “
Operational Deflection Shape of Rotating Object Using Tracking Laser Doppler Vibrometer
,”
2015 IEEE International Conference on Electronics, Circuits, and Systems
,
Cairo, Egypt
,
Dec. 6–9
, pp.
693
696
.
28.
Halkon
,
B. J.
,
Frizzel
,
S. R.
, and
Rothberg
,
S. J.
,
2003
, “
Vibration Measurements Using Continuous Scanning Laser Vibrometry: Velocity Sensitivity Model Experimental Validation
,”
Meas. Sci. Technol.
,
14
(
6
), pp.
773
783
.
29.
Halkon
,
B. J.
, and
Rothberg
,
S. J.
,
2003
, “
Vibration Measurements Using Continuous Scanning Laser Doppler Vibrometry: Theoretical Velocity Sensitivity Analysis With Applications
,”
Meas. Sci. Technol.
,
14
(
3
), p.
382
393
.
30.
Halkon
,
B. J.
, and
Rothberg
,
S. J.
,
2006
, “
Vibration Measurements Using Continuous Scanning Laser Vibrometry: Advanced Aspects in Rotor Applications
,”
Mech. Syst. Signal Process
,
20
(
6
), pp.
1286
1299
.
31.
Castellini
,
P.
, and
Tomasini
,
E. P.
,
2004
, “
Image-Based Tracking Laser Doppler Vibrometer
,”
Rev. Sci. Instrum.
,
75
(
1
), pp.
222
232
.
32.
Lyu
,
L. F.
, and
Zhu
,
W. D.
,
2021
, “
Operational Modal Analysis of a Rotating Structure Under Ambient Excitation Using a Tracking Continuously Scanning Laser Doppler Vibrometer System
,”
Mech. Syst. Signal Process
,
152
(
5
), p.
107367
.
33.
Zhu
,
W. D.
, and
Mote
,
C. D.
, Jr.
,
1997
, “
Dynamic Modeling and Optimal Control of Rotating Euler-Bernoulli Beams
,”
ASME J. Dyn. Syst. Meas. Control
,
119
(
4
), pp.
802
808
.
34.
Meirovitch
,
L.
,
1967
,
Analytical Methods in Vibrations
,
Macmillan Co
.,
New York
.
35.
Jonkman
,
J.
,
Butterfield
,
S.
,
Musial
,
W.
, and
Scott
,
G.
,
2009
, “
Definition of a 5-MW Reference Wind Turbine for Offshore System Development
,”
(No. NREL/TP-500-38060)
,
National Renewable Energy Lab. (NREL)
,
Golden, CO
.
36.
Acar
,
G. D.
, and
Feeny
,
B. F.
,
2018
, “
Bend-Bend-Twist Vibrations of a Wind Turbine Blade
,”
Wind Energy
,
21
(
1
), pp.
15
28
.
You do not currently have access to this content.