In this Part 2 of a two-part series, the experimental verification and comparison of this work are presented. In this paper, the effect of beam-type resonator position on flexible dynamics is determined experimentally. The system is excited using band-limited white noise via electrodynamic shaker, and the data are collected with several transducers and a high-speed camera for each actuator beam mounting location; the first four mode shapes and natural frequencies are determined, and a finite element model (FEM) is developed and updated using these data. An additional set of data is collected using a linear sine chirp forcing function and the updated/experimental frequency response functions (FRFs) and time responses for the base and actuator beam tips are found to correlate. Plots of experimentally determined percent modal strain energy versus attachment position for the first four modes is presented, and a final study is also performed showing the fractional root-mean-square (RMS) strain energy in the actuator with respect to the total system. A final set of data is collected in which the actuator beam is moved up the base beam, the piezoelectric patch of the actuator beam is energized with white noise, and the tip response of the base beam is measured; an RMS base beam velocity versus mount position plot was developed. From this work, it is determined that the most practical/optimal position for the secondary beam to serve as both a sensor and actuator to control base beam tip response over a wide frequency band is in the nondimensionalized range: 0.4e<0.6.

References

References
1.
Peres
,
M. A.
,
Bono
,
R. W.
, and
Brown
,
D. L.
,
2010
, “
Practical Aspects of Shaker Measurements for Modal Testing
,”
International Symposium on Music Acoustics
, Leuven, Belgium, Sept. 20–22, pp.
2539
2550
.
2.
Cloutier
,
D.
,
Avitabile
,
P.
,
Bono
,
R.
, and
Peres
,
M.
,
2009
, “
Shaker/Stinger Effects on Measured Frequency Response Functions
,”
27th International Modal Analysis Conference
, Orlando, FL, Feb. 9–12.
3.
Halvorsen
,
W. G.
, and
Brown
,
D. L.
,
1977
, “
Impulse Technique for Structural Frequency Response Testing
,”
Sound Vib.
,
11
(11), pp.
8
21
.
4.
Warren
,
C.
,
Niezrecki
,
C.
,
Avitabile
,
P.
, and
Pingle
,
P.
,
2011
, “
Comparison of FRF Measurements and Mode Shapes Determined Using Optically Image Based, Laser, and Accelerometer Measurements
,”
Mech. Syst. Signal Process.
,
25
(
6
), pp.
2191
2202
.
5.
Helfrick
,
M. N.
,
Niezrecki
,
C.
,
Avitabile
,
P.
, and
Schmidt
,
T.
,
2011
, “
3D Digital Image Correlation Methods for Full-Field Vibration Measurement
,”
Mech. Syst. Signal Process.
,
25
(
3
), pp.
917
927
.
6.
Lundstrom
,
T.
,
Baqersad
,
J.
, and
Niezrecki
,
C.
,
2015
, “
Monitoring the Dynamics of a Helicopter Main Rotor With High-Speed Stereophotogrammetry
,”
Exp. Tech.
,
40
(3), pp. 907–919.
7.
Lundstrom
,
T.
,
2012
, “Dynamic Measurement and Analysis of Large-Scale Rotating Systems Using Stereophotogrammetry,”
MS thesis
, University of Massachusetts Lowell, Lowell, MA.
8.
Chen
,
J. G.
,
Wadhwa
,
N.
,
Cha
,
Y.-J.
,
Durand
,
F.
,
Freeman
,
W. T.
, and
Buyukozturk
,
O.
,
2015
, “
Modal Identification of Simple Structures With High-Speed Video Using Motion Magnification
,”
J. Sound Vib.
,
345
, pp.
58
71
.
9.
Ewins
,
D. J.
,
1984
,
Modal Testing: Theory and Practice
,
Wiley
,
New York
.
10.
Lundstrom
,
T.
,
Sidoti
,
C.
, and
Jalili
,
N.
,
2015
, “
Dynamic Modeling of Stacked, Multi-Plate Flexible Systems
,”
Exp. Mech.
,
55
(
8
), pp.
1551
1568
.
11.
Avitabile
,
P.
,
Tsuji
,
H.
,
O'Callahan
,
J.
, and
DeClerck
,
J. P.
,
2004
, “
Reallocation of System Mass and Stiffness for Achieving Target Specifications
,”
Int. J. Veh. Noise Vib.
,
1(
1–2
), pp.
97
121
.
12.
Avitabile
,
P.
,
Tsuji
,
H.
,
O'Callahan
,
J.
, and
DeClerck
,
J. P.
,
2005
, “
Reallocation of System Mass and Stiffness for Achieving Target Specifications Using a Superelement/Substructuring Methodology
,”
Int. J. Veh. Noise Vib.
,
1
(
3–4
), pp.
307
327
.
13.
Thomson
,
W.
,
1998
,
Theory of Vibration With Applications
,
Prentice Hall
,
Upper Saddle River, NJ
.
14.
Bashash
,
S.
,
Salehi-Khojin
,
A.
, and
Jalili
,
N.
,
2008
, “
Forced Vibration Analysis of Flexible Euler-Bernoulli Beams With Geometrical Discontinuities
,”
American Control Conference
, Seattle, WA, June 11–13, pp.
4029
4034
.
15.
Edgertronic, 2018, “
SC1 Monochrome Camera
,” Edgertronic.
16.
Lucas
,
B. D.
, and
Kanade
,
T.
,
1981
, “
An Iterative Image Registration Technique With an Application to Stereo Vision
,”
Seventh International Joint Conference on Artificial Intelligence (IJCAI'81)
, Vancouver, BC, Canada, Aug. 24–28, pp.
674
679
.
17.
Tomasi
,
C.
, and
Kanade
,
T.
,
1991
, “Detection and Tracking of Point Features,” Carnegie Mellon University, Pittsburgh, PA, Technical Report No.
CMU-CS-91-132
.
18.
Shi
,
J.
,
1994
, “
Good Features to Track
,” IEEE Computer Society Conference Computer Vision and Pattern Recognition (
CVPR'94
), Seattle, WA, June 21–23, pp.
593
600
.
19.
Kalal
,
Z.
,
Mikolajczyk
,
K.
, and
Matas
,
J.
,
2010
, “
Forward-Backward Error: Automatic Detection of Tracking Failures
,”
20th International Conference on Pattern Recognition Pattern Recognition
(
ICPR
), Istanbul, Turkey, Aug. 23–26, pp.
2756
2759
.
20.
LMS Test.Lab 10A
, 2018, “
Leuven Measurement Systems
,” Leuven, Belgium.
21.
O'Callahan
,
J.
,
Avitabile
,
P.
, and
Riemer
,
R.
,
1989
, “
System Equivalent Reduction Expansion Process (SEREP)
,”
Seventh International Modal Analysis Conference
, Las Vegas, NV, Jan. 30–Feb. 2, pp.
29
37
.
22.
Guyan
,
R. J.
,
1965
, “
Reduction of Stiffness and Mass Matrices
,”
AIAA J.
,
3
(
2
), pp.
380
380
.
23.
Allemang
,
R. J.
, and
Brown
,
D. L.
,
1982
, “
A Correlation Coefficient for Modal Vector Analysis
,”
First International Modal Analysis Conference
, Orlando, FL, Nov. 8–10, pp.
110
116
.
24.
Allemang
,
R. J.
,
1981
, “Investigation of Some Multiple Input/Output Frequency Response Functions Experimental Modal Analysis Techniques,”
Ph.D. dissertation
, University of Cincinnati, Cincinnati, OH.
25.
Allemang
,
R. J.
,
2003
, “
The Modal Assurance Criterion–Twenty Years of Use and Abuse
,”
Sound Vib.
,
37
(
8
), pp.
14
23
.
You do not currently have access to this content.