In recent years, nonlinear vibro-acoustic methods have shown potential to identify defects which are difficult to detect using linear ultrasonic methods. However, these methods come with their own challenges such as frequency dependence, requirement for a high excitation amplitude, and difficulties in distinguishing nonlinearity from defect with nonlinearity from other sources to name a few. This paper aims to study the dependence of nonlinear vibro-acoustic methods for detection of delaminations inside a composite laminate, on the excitation methods and excitation frequencies. It is shown that nonlinear vibro-acoustic methods are highly frequency dependent and commonly used excitation signals which utilize particular values of excitation frequencies might not always lead to a clear distinction between intact and delaminated regions of the specimen. To overcome the frequency dependence, signals based on frequency sweep are used. Interpretation of output response to sweep signals to identify damage is demonstrated using an earlier available approach, and a simpler approach is proposed. It is demonstrated that the damage detection with sweep signal excitations is relatively less dependent on excitation frequency than the conventional excitation methods. The proposed interpretation technique is then applied to specimens with delamination of varying sizes and with delaminations at different depths inside the laminate to demonstrate its effectiveness.

References

1.
Rose
,
J. L.
,
2014
,
Ultrasonic Guided Waves in Solid Media
,
Cambridge University Press
, Cambridge, UK.
2.
Nagy
,
P. B.
,
1991
, “
Ultrasonic Detection of Kissing Bonds at Adhesive Interfaces
,”
J. Adhes. Sci. Technol.
,
5
(
8
), pp.
619
630
.
3.
Kundu
,
T.
,
Maji
,
A.
,
Ghosh
,
T.
, and
Maslov
,
K.
,
1998
, “
Detection of Kissing Bonds by Lamb Waves
,”
Ultrasonics
,
35
(
8
), pp.
573
580
.
4.
Brotherhood
,
C.
,
Drinkwater
,
B.
, and
Guild
,
F.
,
2002
, “
The Effect of Compressive Loading on the Ultrasonic Detectability of Kissing Bonds in Adhesive Joints
,”
J. Nondestr. Eval.
,
21
(
3
), pp.
95
104
.
5.
Brotherhood
,
C.
,
Drinkwater
,
B.
, and
Dixon
,
S.
,
2003
, “
The Detectability of Kissing Bonds in Adhesive Joints Using Ultrasonic Techniques
,”
Ultrasonics
,
41
(
7
), pp.
521
529
.
6.
Teles
,
S. V.
, and
Chimenti
,
D.
,
2008
, “
Closed Disbond Detection in Marine Glass-Epoxy/Balsa Composites
,”
NDT E Int.
,
41
(
2
), pp.
129
136
.
7.
Kumar
,
R. V.
,
Bhat
,
M.
, and
Murthy
,
C.
,
2013
, “
Evaluation of Kissing Bond in Composite Adhesive Lap Joints Using Digital Image Correlation: Preliminary Studies
,”
Int. J. Adhes. Adhes.
,
42
, pp.
60
68
.
8.
Poveromo
,
S. L.
, and
Earthman
,
J. C.
,
2014
, “
Analysis of “Kiss” Bonds Between Composite Laminates
,”
JOM
,
66
(
6
), pp.
970
978
.
9.
Wood
,
M.
,
Charlton
,
P.
, and
Yan
,
D.
,
2014
, “
Ultrasonic Evaluation of Artificial Kissing Bonds in CFRP Composites
,”
e-J. NDT
,
19
(
12
), pp. 1–10.https://www.ndt.net/article/ndtnet/2014/98_Charlton.pdf
10.
Chen
,
B. Y.
,
Soh
,
S. K.
,
Lee
,
H. P.
,
Tay
,
T. E.
, and
Tan
,
V. B. C.
,
2016
, “
A Vibro-Acoustic Modulation Method for the Detection of Delamination and Kissing Bond in Composites
,”
J. Compos. Mater.
,
50
(
22
), pp.
3089
3104
.
11.
Yan
,
D.
,
Drinkwater
,
B. W.
, and
Neild
,
S. A.
,
2009
, “
Measurement of the Ultrasonic Nonlinearity of Kissing Bonds in Adhesive Joints
,”
NDT E Int.
,
42
(
5
), pp.
459
466
.
12.
Yan
,
D.
,
Neild
,
S. A.
, and
Drinkwater
,
B. W.
,
2012
, “
Modelling and Measurement of the Nonlinear Behaviour of Kissing Bonds in Adhesive Joints
,”
NDT E Int.
,
47
, pp.
18
25
.
13.
Nagy, P. B. , McGowan, P. , and Adler, L. , 1990, “
Acoustic Nonlinearities in Adhesive Joints
,”
Review of Progress in Quantitative Nondestructive Evaluation. Review of Progress in Quantitative Nondestructive Evaluation
, D. O. Thompson and D. E. Chimenti, eds., Springer, Boston, MA, pp. 1685–1692.
14.
Rothenfusser
,
M.
,
Mayr
,
M.
, and
Baumann
,
J.
,
2000
, “
Acoustic Nonlinearities in Adhesive Joints
,”
Ultrasonics
,
38
(
1–8
), pp.
322
326
.
15.
Delrue
,
S.
,
Tabatabaeipour
,
M.
,
Hettler
,
J.
, and
Van Den Abeele
,
K.
,
2016
, “
Applying a Nonlinear, Pitch-Catch, Ultrasonic Technique for the Detection of Kissing Bonds in Friction Stir Welds
,”
Ultrasonics
,
68
, pp.
71
79
.
16.
Krohn
,
N.
,
Stoessel
,
R.
, and
Busse
,
G.
,
2002
, “
Acoustic Non-Linearity for Defect Selective Imaging
,”
Ultrasonics
,
40
(
1–8
), pp.
633
637
.
17.
Solodov
,
I. Y.
,
Krohn
,
N.
, and
Busse
,
G.
,
2002
, “
Can: An Example of Nonclassical Acoustic Nonlinearity in Solids
,”
Ultrasonics
,
40
(
1–8
), pp.
621
625
.
18.
Solodov
,
I.
,
Wackerl
,
J.
,
Pfleiderer
,
K.
, and
Busse
,
G.
,
2004
, “
Nonlinear Self-Modulation and Subharmonic Acoustic Spectroscopy for Damage Detection and Location
,”
Appl. Phys. Lett.
,
84
(
26
), pp.
5386
5388
.
19.
Kawashima
,
K.
,
Murase
,
M.
,
Yamada
,
R.
,
Matsushima
,
M.
,
Uematsu
,
M.
, and
Fujita
,
F.
,
2006
, “
Nonlinear Ultrasonic Imaging of Imperfectly Bonded Interfaces
,”
Ultrasonics
,
44
, pp.
e1329
e1333
.
20.
Solodov
,
I.
, and
Busse
,
G.
,
2007
, “
Nonlinear Air-Coupled Emission: The Signature to Reveal and Image Microdamage in Solid Materials
,”
Appl. Phys. Lett.
,
91
(
25
), p.
251910
.
21.
Aymerich
,
F.
, and
Staszewski
,
W.
,
2010
, “
Experimental Study of Impact-Damage Detection in Composite Laminates Using a Cross-Modulation Vibro-Acoustic Technique
,”
Struct. Health Monit.
,
9
(
6
), pp.
541
553
.
22.
Aymerich
,
F.
, and
Staszewski
,
W.
,
2010
, “
Impact Damage Detection in Composite Laminates Using Nonlinear Acoustics
,”
Compos. Part A: Appl. Sci. Manuf.
,
41
(
9
), pp.
1084
1092
.
23.
Polimeno
,
U.
,
Meo
,
M.
,
Almond
,
D.
, and
Angioni
,
S.
,
2010
, “
Detecting Low Velocity Impact Damage in Composite Plate Using Nonlinear Acoustic/Ultrasound Methods
,”
Appl. Compos. Mater.
,
17
(
5
), pp.
481
488
.
24.
Sarens
,
B.
,
Verstraeten
,
B.
,
Glorieux
,
C.
,
Kalogiannakis
,
G.
, and
Van Hemelrijck
,
D.
,
2010
, “
Investigation of Contact Acoustic Nonlinearity in Delaminations by Shearographic Imaging, Laser Doppler Vibrometric Scanning and Finite Difference Modeling
,”
IEEE Trans. Ultrason. Ferroelectr. Freq. Control
,
57
(
6
), pp.
1383
1395
.
25.
Chrysochoidis
,
N. A.
,
Barouni
,
A. K.
, and
Saravanos
,
D. A.
,
2011
, “
Delamination Detection in Composites Using Wave Modulation Spectroscopy With a Novel Active Nonlinear Acousto-Ultrasonic Piezoelectric Sensor
,”
J. Intell. Mater. Syst. Struct.
,
22
(
18
), pp.
2193
2206
.
26.
Solodov
,
I.
,
Döring
,
D.
, and
Busse
,
G.
,
2011
, “
New Opportunities for NDT Using Non-Linear Interaction of Elastic Waves With Defects
,”
Strojniški Vestn.-J. Mech. Eng.
,
57
(
3
), pp.
169
182
.http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.161.6275&rep=rep1&type=pdf
27.
Delrue
,
S.
, and
Van Den Abeele
,
K.
,
2012
, “
Three-Dimensional Finite Element Simulation of Closed Delaminations in Composite Materials
,”
Ultrasonics
,
52
(
2
), pp.
315
324
.
28.
Ciampa
,
F.
,
Onder
,
E.
,
Barbieri
,
E.
, and
Meo
,
M.
,
2014
, “
Detection and Modelling of Nonlinear Elastic Response in Damaged Composite Structures
,”
J. Nondestr. Eval.
,
33
(
4
), pp.
515
521
.
29.
Klepka
,
A.
,
Pieczonka
,
L.
,
Staszewski
,
W.
, and
Aymerich
,
F.
,
2014
, “
Impact Damage Detection in Laminated Composites by Non-Linear Vibro-Acoustic Wave Modulations
,”
Compos. Part B: Eng.
,
65
, pp.
99
108
.
30.
Delrue
,
S.
,
Tabatabaeipour
,
M.
,
Hettler
,
J.
, and
van Den Abeele
,
K.
,
2015
, “
Non-Destructive Evaluation of Kissing Bonds Using Local Defect Resonance (LDR) Spectroscopy: A Simulation Study
,”
Phys. Procedia
,
70
, pp.
648
651
.
31.
Eckel
,
S.
,
Meraghni
,
F.
,
Pomarede
,
P.
, and
Declercq
,
N. F.
,
2016
, “
Nondestructive Testing of Composites Using a Nonlinear Acoustic Spectroscopy Method
,” 17th European Conference on Composite Materials (
ECCM17
), Munich, Germany.https://sam.ensam.eu/handle/10985/11179
32.
Eckel
,
S.
,
Meraghni
,
F.
,
Pomaréde
,
P.
, and
Declercq
,
N. F.
,
2017
, “
Investigation of Damage in Composites Using Nondestructive Nonlinear Acoustic Spectroscopy
,”
Exp. Mech.
,
57
(
2
), pp.
207
217
.
33.
Singh
,
A. K.
,
Chen
,
B. Y.
,
Tan
,
V. B. C.
,
Tay
,
T. E.
, and
Lee
,
H. P.
,
2017
, “
Finite Element Modeling of Nonlinear Acoustics/Ultrasonics for the Detection of Closed Delaminations in Composites
,”
Ultrasonics
,
74
, pp.
89
98
.
34.
Singh
,
A. K.
,
Chen
,
B. Y.
,
Tan
,
V. B. C.
,
Tay
,
T. E.
, and
Lee
,
H. P.
,
2017
, “
A Theoretical and Numerical Study on the Mechanics of Vibro-Acoustic Modulation
,”
J. Acoust. Soc. Am.
,
141
(
4
), pp.
2821
2831
.
35.
Donskoy
,
D. M.
,
Ferroni
,
K.
,
Sutin
,
A.
, and
Sheppard
,
K.
,
1998
,
A Nonlinear Acoustic Technique for Crack and Corrosion Detection in Reinforced Concrete
,
Springer
, Boston, MA, pp.
555
560
.
36.
Bruno
,
C. L. E.
,
Gliozzi
,
A. S.
,
Scalerandi
,
M.
, and
Antonaci
,
P.
,
2009
, “
Analysis of Elastic Nonlinearity Using the Scaling Subtraction Method
,”
Phys. Rev. B
,
79
(
6
), p.
064108
.
37.
Antonaci
,
P.
,
Bruno
,
C. L. E.
,
Bocca
,
P. G.
,
Scalerandi
,
M.
, and
Gliozzi
,
A.
,
2010
, “
Nonlinear Ultrasonic Evaluation of Load Effects on Discontinuities in Concrete
,”
Cem. Concr. Res.
,
40
(
2
), pp.
340
346
.
38.
Antonaci
,
P.
,
Bruno
,
C. L. E.
,
Gliozzi
,
A.
, and
Scalerandi
,
M.
,
2010
, “
Monitoring Evolution of Compressive Damage in Concrete With Linear and Nonlinear Ultrasonic Methods
,”
Cem. Concr. Res.
,
40
(
7
), pp.
1106
1113
.
39.
Antonaci
,
P.
,
Bruno
,
C. L. E.
,
Gliozzi
,
A.
, and
Scalerandi
,
M.
,
2010
, “
Evolution of Damage-Induced Nonlinearity in Proximity of Discontinuities in Concrete
,”
Int. J. Solids Struct.
,
47
(
11–12
), pp.
1603
1610
.
40.
Ongpeng
,
J. M. C.
,
Oreta
,
W. C.
, and
Hirose
,
S.
,
2016
, “
Effect of Load Pattern in the Generation of Higher Harmonic Amplitude in Concrete Using Nonlinear Ultrasonic Test
,”
J. Adv. Concr. Technol.
,
14
(
5
), pp.
205
214
.
41.
Tranquart
,
F.
,
Grenier
,
N.
,
Eder
,
V.
, and
Pourcelot
,
L.
,
1999
, “
Clinical Use of Ultrasound Tissue Harmonic Imaging
,”
Ultrasound Med. Biol.
,
25
(
6
), pp.
889
894
.
42.
Duck
,
F. A.
,
2002
, “
Nonlinear Acoustics in Diagnostic Ultrasound
,”
Ultrasound Med. Biol.
,
28
(
1
), pp.
1
18
.
43.
Renaud
,
G.
,
Callé
,
S.
,
Remenieras
,
J.-P.
, and
Defontaine
,
M.
,
2008
, “
Non-Linear Acoustic Measurements to Assess Crack Density in Trabecular Bone
,”
Int. J. Non-Linear Mech.
,
43
(
3
), pp.
194
200
.
44.
Andreaus
,
U.
,
Casini
,
P.
, and
Vestroni
,
F.
,
2007
, “
Non-Linear Dynamics of a Cracked Cantilever Beam Under Harmonic Excitation
,”
Int. J. Non-Linear Mech.
,
42
(
3
), pp.
566
575
.
45.
Donskoy
,
D.
,
Sutin
,
A.
, and
Ekimov
,
A.
,
2001
, “
Nonlinear Acoustic Interaction on Contact Interfaces and Its Use for Nondestructive Testing
,”
NDT E Int.
,
34
(
4
), pp.
231
238
.
46.
Hu
,
H.
,
Staszewski
,
W.
,
Hu
,
N.
,
Jenal
,
R.
, and
Qin
,
G.
,
2010
, “
Crack Detection Using Nonlinear Acoustics and Piezoceramic Transducers—Instantaneous Amplitude and Frequency Analysis
,”
Smart Mater. Struct.
,
19
(
6
), p.
065017
.
47.
Klepka
,
A.
,
Staszewski
,
W.
,
Jenal
,
R.
,
Szwedo
,
M.
,
Iwaniec
,
J.
, and
Uhl
,
T.
,
2012
, “
Nonlinear Acoustics for Fatigue Crack Detection—Experimental Investigations of Vibro-Acoustic Wave Modulations
,”
Struct. Health Monit.
,
11
(
2
), pp.
197
211
.
48.
Meo
,
M.
, and
Zumpano
,
G.
,
2005
, “
Nonlinear Elastic Wave Spectroscopy Identification of Impact Damage on a Sandwich Plate
,”
Compos. Struct.
,
71
(
3–4
), pp.
469
474
.
49.
Parsons
,
Z.
, and
Staszewski
,
W.
,
2006
, “
Nonlinear Acoustics With Low-Profile Piezoceramic Excitation for Crack Detection in Metallic Structures
,”
Smart Mater. Struct.
,
15
(
4
), p.
1110
.
50.
Pieczonka
,
L.
,
Ukowski
,
P.
,
Klepka
,
A.
,
Staszewski
,
W.
,
Uhl
,
T.
, and
Aymerich
,
F.
,
2014
, “
Impact Damage Detection in Light Composite Sandwich Panels Using Piezo-Based Nonlinear Vibro-Acoustic Modulations
,”
Smart Mater. Struct.
,
23
(
10
), p.
105021
.
51.
Yoder
,
N. C.
, and
Adams
,
D. E.
,
2010
, “
Vibro-Acoustic Modulation Utilizing a Swept Probing Signal for Robust Crack Detection
,”
Struct. Health Monit.
,
9
(
3
), pp.
257
267
.
52.
Sohn
,
H.
,
Lim
,
H. J.
,
DeSimio
,
M. P.
,
Brown
,
K.
, and
Derriso
,
M.
,
2014
, “
Nonlinear Ultrasonic Wave Modulation for Online Fatigue Crack Detection
,”
J. Sound Vib.
,
333
(
5
), pp.
1473
1484
.
53.
Dutta
,
D.
,
Sohn
,
H.
,
Harries
,
K. A.
, and
Rizzo
,
P.
,
2009
, “
A Nonlinear Acoustic Technique for Crack Detection in Metallic Structures
,”
Struct. Health Monit.
,
8
(
3
), pp.
251
262
.
54.
Singh
,
A. K.
,
Tan
,
V. B. C.
,
Tay
,
T. E.
, and
Lee
,
H. P.
,
2016
, “
A Novel Nonlinear Acoustics Technique for the Detection of Defects in Composite Laminates
,”
Eighth International Symposium on NDT in Aerospace
, Bangalore, India, Nov. 3–5.https://www.ndt.net/article/aero2016/papers/AshishKumarSingh_VincentBCTan_TongEarnTay_HeowPuehLee.pdf
55.
Singh
,
A. K.
,
Tan
,
V. B. C.
,
Tay
,
T. E.
, and
Lee
,
H. P.
,
2017
, “
A Numerical Study on the Applicability of Nonlinear Acoustics Methods for Damage Imaging in Composite Laminates
,”
21st International Conference on Composite Materials
, Xi'an, China, Aug. 20–25.http://www.iccm-central.org/Proceedings/ICCM21proceedings/papers/4272.pdf
56.
Klepka
,
A.
,
Adamczyk
,
M.
,
Pieczonka
,
L.
, and
Staszewski
,
W.
,
2016
, “
Wideband Excitation in Nonlinear Vibro-Acoustic Modulation for Damage Detection
,”
Proc. SPIE
,
9805
, p. 980513.
57.
Rahammer
,
M.
, and
Kreutzbruck
,
M.
,
2017
, “
Fourier-Transform Vibrothermography with Frequency Sweep Excitation Utilizing Local Defect Resonances
,”
NDT E Int.
,
86
, pp.
83
88
.
58.
Lim
,
H. J.
,
Sohn
,
H.
,
DeSimio
,
M. P.
, and
Brown
,
K.
,
2014
, “
Reference-Free Fatigue Crack Detection Using Nonlinear Ultrasonic Modulation Under Various Temperature and Loading Conditions
,”
Mech. Syst. Signal Process.
,
45
(
2
), pp.
468
478
.
59.
Lingvall
,
F.
, and
Skoglund
,
E.
,
2015
, “
DolphiCam 1.3
,” Dolphitech, Raufoss, Norway,
Technical Paper
http://www.dolphitech.com/wp-content/uploads/2014/12/dolphicam_whitepaper_4401.pdf.
60.
3M,
2016
, “
3M Scotch-Weld DP420 Technical Data
,” 3M Company, Maplewood, MN,
Technical Data
.http://multimedia.3m.com/mws/media/66998O/scotch-weldtm-epoxy-adhesive-dp420-blck-ns-blck-offwhit-lh.pdf?fn=420.pdf
61.
PI,
2018
, “
PI Piezoelectric discs datasheet
,”
Physik Instrumente (PI) GmbH, Karlsruhe, Germany.
62.
APC International,
2018
, “
APC Piezoelectric Calculator
,”
APC International, Mackeyville, PA.
63.
Giurgiutiu
,
V.
,
2007
,
Structural Health Monitoring: With Piezoelectric Wafer Active Sensors
, Elsevier, New York.
64.
Amerini
,
F.
, and
Meo
,
M.
,
2011
, “
Structural Health Monitoring of Bolted Joints Using Linear and Nonlinear Acoustic/Ultrasound Methods
,”
Struct. Health Monit.
,
10
(
6
), pp.
659
672
.
65.
Dehghan-Niri
,
E.
, and
Al-Beer
,
H.
,
2018
, “
Phase-Space Topography Characterization of Nonlinear Ultrasound Waveforms
,”
Ultrasonics
,
84
, pp. 446–458.
66.
Guyer
,
R. A.
, and
Johnson
,
P. A.
,
1999
, “
Nonlinear Mesoscopic Elasticity: Evidence for a New Class of Materials
,”
Phys. Today
,
52
(
4
), pp.
30
36
.
67.
Van Den Abeele
,
K. E.
,
Sutin
,
A.
,
Carmeliet
,
J.
, and
Johnson
,
P. A.
,
2001
, “
Micro-Damage Diagnostics Using Nonlinear Elastic Wave Spectroscopy (News)
,”
NDT E Int.
,
34
(
4
), pp.
239
248
.
68.
Burlayenko
,
V.
, and
Sadowski
,
T.
,
2012
, “
Finite Element Nonlinear Dynamic Analysis of Sandwich Plates With Partially Detached Facesheet and Core
,”
Finite Elem. Anal. Des.
,
62
, pp.
49
64
.
69.
Delrue
,
S.
,
Aleshin
,
V.
,
Truyaert
,
K.
,
Matar
,
O. B.
, and
Van Den Abeele
,
K.
,
2018
, “
Two Dimensional Modeling of Elastic Wave Propagation in Solids Containing Cracks With Rough Surfaces and Friction–Part II: Numerical Implementation
,”
Ultrasonics
,
82
, pp.
19
30
.
70.
Delrue
,
S.
, and
Van Den Abeele
,
K.
,
2015
, “
Detection of Defect Parameters Using Nonlinear Air-Coupled Emission by Ultrasonic Guided Waves at Contact Acoustic Nonlinearities
,”
Ultrasonics
,
63
, pp.
147
154
.
71.
Kögl
,
M.
,
Hurlebaus
,
S.
, and
Gaul
,
L.
,
2004
, “
Finite Element Simulation of Non-Destructive Damage Detection With Higher Harmonics
,”
NDT E Int.
,
37
(
3
), pp.
195
205
.
72.
Wan
,
X.
,
Zhang
,
Q.
,
Xu
,
G.
, and
Tse
,
P. W.
,
2014
, “
Numerical Simulation of Nonlinear Lamb Waves Used in a Thin Plate for Detecting Buried Micro-Cracks
,”
Sensors
,
14
(
5
), pp.
8528
8546
.
73.
Yuan
,
M.
,
Lee
,
T.
,
Kang
,
T.
,
Zhang
,
J.
,
Song
,
S.-J.
, and
Kim
,
H.-J.
,
2015
, ”
Absolute Measurement of Ultrasonic Non-Linearity Parameter at Contact Interface
,”
Nondestr. Test. Eval.
,
30
(
4
), pp.
356
372
.
74.
Zhao
,
Y.
,
Li
,
F.
,
Cao
,
P.
,
Liu
,
Y.
,
Zhang
,
J.
,
Fu
,
S.
,
Zhang
,
J.
, and
Hu
,
N.
,
2017
, “
Generation Mechanism of Nonlinear Ultrasonic Lamb Waves in Thin Plates With Randomly Distributed Micro-Cracks
,”
Ultrasonics
,
79
, pp.
60
67
.
75.
Duffour
,
P.
,
Morbidini
,
M.
, and
Cawley
,
P.
,
2006
, “
A Study of the Vibro-Acoustic Modulation Technique for the Detection of Cracks in Metals
,”
J. Acoust. Soc. Am.
,
119
(
3
), pp.
1463
1475
.
76.
Duffour
,
P.
,
Morbidini
,
M.
, and
Cawley
,
P.
,
2006
, “
Comparison Between a Type of Vibro-Acoustic Modulation and Damping Measurement as NDT Techniques
,”
NDT E Int.
,
39
(
2
), pp.
123
131
.
77.
Pieczonka
,
L.
,
Klepka
,
A.
,
Martowicz
,
A.
, and
Staszewski
,
W. J.
,
2016
, “
Nonlinear Vibroacoustic Wave Modulations for Structural Damage Detection: An Overview
,”
Opt. Eng.
,
55
(
1
), p.
011005
.
78.
Zaitsev
,
V.
,
Nazarov
,
V.
,
Gusev
,
V.
, and
Castagnede
,
B.
,
2006
, “
Novel Nonlinear-Modulation Acoustic Technique for Crack Detection
,”
NDT E Int.
,
39
(
3
), pp.
184
194
.
79.
Scalerandi
,
M.
,
Gliozzi
,
A.
,
Bruno
,
C. L. E.
,
Masera
,
D.
, and
Bocca
,
P.
,
2008
, “
A Scaling Method to Enhance Detection of a Nonlinear Elastic Response
,”
Appl. Phys. Lett.
,
92
(
10
), p.
101912
.
80.
Scalerandi
,
M.
,
Gliozzi
,
A. S.
,
Bruno
,
C. L. E.
, and
Van Den Abeele
,
K.
,
2008
, “
Nonlinear Acoustic Time Reversal Imaging Using the Scaling Subtraction Method
,”
J. Phys. D: Appl. Phys.
,
41
(
21
), p.
215404
.
81.
Tabatabaeipour
,
M.
,
Hettler
,
J.
,
Delrue
,
S.
, and
Van Den Abeele
,
K.
,
2017
, “
Visualization of Delaminations in Composite Structures Using a Baseline-Free, Sparse Array Imaging Technique Based on Nonlinear Lamb Wave Propagation
,”
Acta Acust. Acust.
,
103
(
6
), pp.
987
997
.
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