The evaluation of structural power flow (or structural intensity (SI)) in engineering structures is a field of increasing interest in connection with vibration analysis and noise control. In contrast to classical techniques such as modal analysis, the SI indicates the magnitude and direction of the vibratory energy traveling in the structures, which yields information about the positions of the sources/sinks, along with the energy transmission path. In this paper, a new algorithm is proposed to model operational deflection shapes (ODS). The model is a two-dimensional Fourier domain model that is estimated by using a weighted nonlinear least-squares method. From the wave number-frequency domain data thus obtained, the spatial derivatives that are necessary to determine the structural power flow are easily computed. The proposed method is less sensitive to measurement noise than traditional power flow estimation techniques. A numerical model of a simply supported plate excited by two shakers, phased to act as an energy source and sink, is used as a simulation case. Measurements are executed on a clamped plate excited by an electromagnetic shaker in combination with a damper.

References

References
1.
Pavic
,
G.
,
1976
, “
Measurement of Structure Borne Wave Intensity—Part I: Formulation of the Methods
,”
J. Sound Vib.
,
49
(
2
), pp.
221
230
.10.1016/0022-460X(76)90498-3
2.
Arruda
,
J. R.
F.
and
Mas
,
P.
,
1998
, “
Localizing Energy Sources and Sinks in Plates Using Power Flow Maps Computed From Laser Vibrometer Measurements
,”
Shock Vib.
,
5
, pp.
235
253
.
3.
Blotter
,
J. D.
,
West
,
R. L.
, and
Sommerfeldt
,
S. D.
,
2002
, “
Spatially Continuous Power Flow Using a Scanning Laser Doppler Vibrometer
,”
ASME J. Vibr. Acoust.
,
124
, pp.
476
482
.10.1115/1.1497363
4.
Noiseux
,
D. U.
,
1970
, “
Measurement of Power Flow in Uniform Beams and Plates
,”
J. Acoust. Soc. Am.
,
47
(
1
), pp.
238
247
.10.1121/1.1911472
5.
Zhang
,
Y.
and
Mann
,
J. A.
,
1996
, “
Measuring the Structural Intensity and Force Distribution in Plates
,”
J. Acoust. Soc. Am.
,
99
(
1
), pp.
345
353
.10.1121/1.414546
6.
Zhang
,
Y.
and
Mann
,
J. A.
,
1996
, “
Examples of Using Structural Intensity and the Force Distribution to Study Vibrating Plates
,”
J. Acoust. Soc. Am.
,
99
(
1
), pp.
354
361
.10.1121/1.414547
7.
Daley
,
M. J.
and
Hambric
,
S. A.
,
2005
, “
Simulating and Measuring Structural Intensity Fields in Plates Induced by Spatially and Temporally Random Excitation
,”
ASME J. Vibr. Acoust.
127
, pp.
451
457
.10.1115/1.2013299
8.
Pascal
,
J. C.
,
Carniel
,
X.
, and
Li
,
J. F.
,
2006
, “
Characterisation of a Dissipative Assembly Using Structural Intensity Measurements and Energy Conservation Equation
,”
Mech. Syst. Signal Process.
,
20
, pp.
1300
1311
.10.1016/j.ymssp.2005.11.012
9.
Peng
,
S. Z.
,
2007
, “
Laser Doppler Vibrometer for Mode Shape and Power Flow Analysis in Coupled Structures
,”
Int. J. Veh. Noise Vib.
,
3
(
1
), pp.
70
87
.10.1504/IJVNV.2007.014401
10.
Pascal
,
J. C.
,
Loyau
,
T.
, and
Carniel
,
X.
,
1993
, “
Complete Determination of Structural Intensity in Plates Using Laser Vibrometers
,”
J. Sound Vib.
,
161
(
3
), pp.
527
531
.10.1006/jsvi.1993.1090
11.
Pascal
,
J. C.
,
Li
,
J. F.
, and
Carniel
,
X.
,
2002
, “
Wavenumber Processing Techniques to Determine Structural Intensity and its Divergence From Optical Measurements Without Leakage Effects
,”
Shock Vib.
,
9
, pp.
57
66
.
12.
Arruda
,
J. R. F.
,
1992
, “
Surface Smoothing and Partial Spatial Derivates Computation Using a Regressive Discrete Fourier Series
,”
Mech. Syst. Signal Process.
,
6
(
1
), pp.
41
50
.10.1016/0888-3270(92)90055-N
13.
Arruda
,
J. R. F.
,
do Rio
,
S. A. V.
, and
Santos
,
L. A. S. B.
,
1996
, “
A Space-Frequency Data Compression Method for Spatially Dense Laser Doppler Vibrometer Measurements
,”
Shock Vib.
,
3
(
2
), pp.
127
133
.
14.
Du
,
J.
,
Liu
,
Z.
,
Li
,
W.
,
Zhang
,
X.
, and
Li
,
W.
,
2010
, “
Free In-Plane Vibration Analysis of Rectangular Plates With Elastically Point-Supported Edges
,”
ASME J. Vibr. Acoust.
,
132
, p.
031002
.10.1115/1.4000777
15.
Vanherzeele
,
J.
,
Guillaume
,
P.
,
Vanlanduit
,
S.
, and
Verboven
,
P.
,
2006
, “
Data Reduction Using a Generalized Regressive Discrete Fourier Series
,”
J. Sound Vib.
,
298
, pp.
1
11
.10.1016/j.jsv.2006.03.052
16.
Vanherzeele
,
J.
,
Vanlanduit
,
S.
, and
Guillaume
,
P.
,
2008
, “
Reducing Spatial Data Using an Optimized Regressive Discrete Fourier Series
,”
J. Sound Vib.
,
309
, pp.
858
867
.10.1016/j.jsv.2007.07.066
17.
Vanherzeele
,
J.
,
2007
, “
Design of Regressive Fourier Techniques for Processing Optical Measurements
,” PhD thesis,
Vrije Universiteit Brussel
,
Brussels
.
18.
Guillaume
,
P.
,
Verboven
,
P.
, and
Vanlanduit
,
S.
,
1998
, “
Frequency-Domain Maximum Likelihood Identification of Modal Parameters With Confidence Intervals
,”
Proceedings of ISMA 23, Noise and Vibration Engineering, K. U. Leuven, Belgium, September 16-18
, pp.
359
376
.
19.
Leissa
,
A. W.
,
1969
,
Vibration of Plates
,
National Aeronautics and Space Administration
,
Washington, D.C.
20.
Verboven
,
P.
,
Parloo
,
E.
,
Guillaume
,
P.
, and
Van Overmeire
,
M.
,
2002
, “
Autonomous Structural Health Monitoring—Part I: Modal Parameter Estimation and Tracking
,”
Mech. Syst. Signal Process.
,
16
(
4
), pp.
637
657
.10.1006/mssp.2002.1492
21.
Vanlanduit
,
S.
,
Verboven
,
P.
,
Guillaume
,
P.
, and
Schoukens
,
J.
,
2003
, “
An Automatic Frequency Domain Modal Parameter Estimation Algorithm
,”
J. Sound Vib.
,
265
, pp.
647
661
.10.1016/S0022-460X(02)01461-X
22.
Verboven
,
P.
,
Guillaume
,
P.
,
Cauberghe
,
B.
,
Parloo
,
E.
, and
Vanlanduit
,
S.
,
2003
, “
Stabilization Charts and Uncertainty Bounds for Frequency-Domain Linear Least Squares Estimators
,”
Proceedings of the IMAC-XXI Conference and Exposition on Structural Dynamics
,
Feb
.
3
6
.
23.
Vuye
,
C.
,
2011
, “
Measurement and Modeling of Sound and Vibration Fields Using a Scanning Laser Doppler Vibrometer
,” PhD thesis,
Vrije Universiteit Brussel
,
Brussels
.
24.
Gavric
,
L.
and
Pavic
,
G.
,
1993
, “
A Finite Element Method for Computation of Structural Intensity by the Normal Mode
,”
J. Sound Vib.
,
164
(
1
), pp.
29
43
.10.1006/jsvi.1993.1194
25.
Gavric
,
L.
,
Carlsson
,
U.
, and
Feng
,
L.
,
1997
, “
Measurement of Structural Intensity Using a Normal Mode Approach
,”
J. Sound Vib.
,
206
(
1
), pp.
87
101
.10.1006/jsvi.1997.1077
26.
Arruda
,
J.
and
Mas
,
P.
,
1996
, “
Predicting and Measuring Flexural Power Flow in Plates
,”
Proceedings of the 2nd International Conference on Vibration Measurements by Laser Techniques
,
Sept
.
23–25
, SPIE,
2868
, pp.
149
163
.
27.
Vanlanduit
,
S.
,
Guillaume
,
P.
, and
Schoukens
,
J.
,
2004
, “
Robust Data Reduction of High Spatial Resolution Optical Vibration Measurements
,”
J. Sound Vib.
,
274
(
1–2
), pp.
369
384
.10.1016/j.jsv.2003.05.020
28.
Golub
,
G.
H.
and
Van
Loan
,
C. F.
,
1996
,
Matrix Computations
(
Johns Hopkins Studies in Mathematical Sciences
),
3rd ed., Johns Hopkins University Press, Baltimore, MD.
You do not currently have access to this content.