This paper presents a modeling approach for estimating time varying loads acting on a component from experimental strain measurements. The strain response of an elastic vibrating system is written as a linear superposition of strain modes. Since the strain modes, as well as the normal displacement modes, are intrinsic dynamic characteristics of a component, the dynamic loads exciting a component are estimated by measuring induced strain fields. The accuracy of the estimated loads depends on a number of factors, such as the placement locations and orientations of the gauges on the instrumented structure, as well as the number of retained modes from strain modal analysis. A solution procedure based on the construction of D-optimal designs is implemented to determine the optimum locations and orientations of strain gauges such that the variance in load estimates is minimized. A numerical as well as an experimental validation of the proposed approach through two example problems is also presented.

References

References
1.
Ewins
,
D. J.
,
2000
,
Modal Testing: Theory, Practice, and Applications
,
Research Studies Press Ltd.
,
Baldock, UK
.
2.
Hillary
,
B.
, and
Ewins
,
D. J.
,
1984
, “
The Use of Strain Gages in Force Determination and Frequency Response Function
,”
Proceedings of the 2nd International Modal Analysis Conference (IMAC)
,
Orlando, FL
, February 6–9, pp.
627
634
.
3.
Bernasconi
,
O.
, and
Ewins
,
D. J.
,
1989
, “
Modal Strain/Stress Fields
,”
J. Modal Anal.
,
4
(
2
), pp.
68
76
.
4.
Li
,
D. B.
,
Zhuge
,
H.
, and
Wang
,
B.
,
1989
, “
The Principles and Techniques of Experimental Strain Modal Analysis
,”
Proceedings of the 7th International Modal Analysis Conference (IMAC)
,
Las Vegas, NV
, January 30-February 2, pp.
1285
1289
.
5.
Tsang
,
W. F.
,
1990
, “
Use of Dynamic Strain Measurements for the Modeling of Structures
,”
Proceedings of the 8th International Modal Analysis Conference (IMAC)
,
Kissimmee, FL
, January 29-February 1, pp.
1246
1251
.
6.
Yam
,
L. H.
,
Leung
,
T. P.
,
Li
,
D. B.
, and
Xue
,
K. Z.
,
1996
, “
Theoretical and Experimental Study of Modal Strain Analysis
,”
J. Sound Vib.
,
191
(
2
), pp.
251
260
.10.1006/jsvi.1996.0119
7.
Sommerfeld
,
J. L.
, and
Meyer
,
R. A.
,
1999
, “
Correlation and Accuracy of a Wheel Force Transducer as Developed and Tested on a Flat-Trac® Tire Test System
,”
SAE
Paper No. 1999-01-0938.10.4271/1999-01-0938
8.
Masroor
,
S. A.
, and
Zachary
,
L. W.
,
1990
, “
Designing an All-Purpose Force Transducer
,”
Exp. Mech.
,
31
(
1
), pp.
33
35
.10.1007/BF02325720
9.
Wickham
,
M. J.
,
Riley
,
D. R.
, and
Nachtsheim
,
C. J.
,
1995
, “
Integrating Optimal Experimental Design Into the Design of a Multi-Axis Load Transducer
,”
ASME J. Eng. Ind.
,
117
(
3
), pp.
400
405
.10.1115/1.2804346
10.
Szwedowicz
,
J.
,
Senn
,
S. M.
, and
Abhari
,
R. S.
,
2002
, “
Optimum Strain Gage Application to Bladed Assemblies
,”
ASME J. Turbomach.
,
124
(
4
), pp.
606
613
.10.1115/1.1506957
11.
Mignolet
,
M. P.
, and
Choi
,
B. K.
,
2003
, “
Robust Optimal Positioning of Strain Gages on Blades
,”
ASME J. Turbomach.
,
125
(
1
), pp.
155
164
.10.1115/1.1509076
12.
Galil
,
Z.
, and
Kiefer
,
J.
,
1980
, “
Time- and Space-Saving Computer Methods, Related to Mitchell's DETMAX, for Finding D-Optimum Designs
,”
Technometrics
,
22
(
3
), pp.
301
313
.10.1080/00401706.1980.10486161
13.
Mitchell
,
T. J.
,
1974
, “
An Algorithm for the Construction of D-Optimal Experimental Designs
,”
Technometrics
,
16
(
2
), pp.
203
210
.10.2307/1267940
14.
Atkinson
,
A. C.
, and
Donev
,
A. N.
,
1992
,
Optimum Experimental Designs
,
Oxford University Press
,
New York
.
15.
Budynas
,
R. G.
,
1999
,
Advanced Strength and Applied Stress Analysis
,
2nd ed.
,
McGraw-Hill
,
New York
.
16.
Chatterjee
,
S.
, and
Hadi
,
A. S.
,
1988
,
Sensitivity Analysis in Linear Regression
,
John Wiley
,
New York
.
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