Acoustoelastic techniques have been recently used to characterize the state of prestress in structures such as plates. The velocity of guided wave modes propagating through plates is sensitive to the magnitude and orientation of the initial state of stress. Dispersion curves for phase velocities of plate guided waves can be computed using the superposition of partial bulk waves (SPBW) method. Here, a semi-analytical finite element (SAFE) method is formulated for the acoustoelastic problem of guided waves in weakly nonlinear elastic plates. The SAFE formulation is shown to provide phase velocity dispersion curve results identical with those provided by the SPBW method for the problem of a plate under a uniaxial and uniform tensile stress. Analytical phase and group velocity dispersion curves are also obtained for a plate with an initial prestress gradient through its thickness using the SAFE method. The magnitude of the prestress gradient is shown to have a significant effect on phase and group velocities of the fundamental and first order Lamb modes, only in certain frequency-thickness regimes.

1.
Z.
Su
and
L.
Ye
,
Identification of Damage Using Lamb Waves
(
Springer-Verlag
,
Berlin Heidelberg
,
2009
).
2.
W. J.
Staszewski
,
S.
Mahzan
, and
R.
Traynor
, “
Health monitoring of aerospace composite structures-active and passive approach
,”
Compos. Sci. Technol.
69
,
1678
1685
(
2009
).
3.
A.
Raghavan
and
C. E. S.
Cesnik
, “
Review of guided wave structural health monitoring
,”
Shock Vib. Dig.
39
(
2
),
91
114
(
2007
).
4.
Z.
Su
,
L.
Ye
, and
Y.
Lu
, “
Guided Lamb waves for identification of damage in composite structures: A review
,”
J. Sound Vib.
295
,
753
780
(
2006
).
5.
F.
Yan
,
R. L.
Royer
, and
J. L.
Rose
, “
Ultrasonic guided wave imaging techniques in structural health monitoring
,”
J. Intell. Mater. Syst. Struct.
21
,
377
384
(
2010
).
6.
C. H.
Wang
,
J. T.
Rose
, and
F. K.
Chang
, “
A synthetic time reversal imaging method for structural health monitoring
,”
Smart Mater. Struct.
13
,
415
423
(
2004
).
7.
E. B.
Flynn
,
M. D.
Todd
,
P. D.
Wilcox
,
B. W.
Drinkwater
, and
A. J.
Croxford
, “
Maximum likelihood estimation of damage location in guided wave structural health monitoring
,”
Proc. R. Soc. A
467
,
2575
2596
(
2011
).
8.
R. A.
Toupin
and
B.
Bernstein
, “
Sound waves in deformed perfectly elastic materials. Acoustoelastic effect
,”
J. Acoust Soc. Am.
33
(
2
),
216
225
(
1961
).
9.
D. S.
Hughes
and
J. L.
Kelly
, “
Second order elastic deformation of solids
,”
Phys. Rev.
92
(
5
),
1145
1149
(
1953
).
10.
Y. H.
Pao
and
U.
Gamer
, “
Acoustoelastic waves in orthotropic media
,”
J. Acoust. Soc. Am.
77
(
3
),
806
812
(
1985
).
11.
P.
Kayestha
,
A. C.
Wijeyewickrema
, and
K.
Kishimoto
, “
Wave propagation along a non-principal direction in a compressible pre-stressed elastic layer
,”
Int. J. Solids Struct.
48
,
2141
2153
(
2011
).
12.
D.
Husson
, “
A perturbation theory for the acoustoelastic effect of surface waves
,”
J. Appl. Phys.
57
(
5
),
1562
1568
(
1985
).
13.
F.
Chen
and
P. D.
Wilcox
, “
The effect of load on guided wave propagation
,”
Ultrasonics
47
,
111
122
(
2007
).
14.
N.
Gandhi
,
J. E.
Michaels
, and
S. J.
Lee
, “
Acoustoelastic Lamb wave propagation in biaxially stressed plates
,”
J. Acoust. Soc. Am.
132
(
3
),
1284
1293
(
2012
).
15.
A. H.
Nayfeh
,
Wave Propagation in Layered Anisotropic Media
(
Elsevier
,
Amsterdam
,
1995
).
16.
M.
Mazzotti
,
A.
Marzani
,
I.
Bartoli
, and
E.
Viola
, “
Guided waves dispersion analysis for prestressed viscoelastic waveguides by means of the safe method
,”
Int. J. Solids Struct.
49
,
2359
2372
(
2012
).
17.
N.
Pei
and
L.
Bond
, “
Higher order acoustoelastic Lamb wave propagation in stressed plates
,”
J. Acoust. Soc. Am.
140
(
5
),
3834
3843
(
2016
).
18.
N.
Pei
and
L.
Bond
, “
Comparison of acoustoelastic Lamb wave propagation in stressed plates for different measurement orientations
,”
J. Acoust. Soc. Am.
142
(
4
),
EL327
EL331
(
2017
).
19.
A. C.
Kubrusly
,
A. M. B.
Braga
, and
J. P.
von der Weid
, “
Derivation of acoustoelastic Lamb wave dispersion curves in anisotropic plates at the initial and natural frames of reference
,”
J. Acoust. Soc. Am.
140
(
4
),
2412
2417
(
2016
).
20.
M.
Lematre
,
G.
Feuillard
,
E. L.
Clezio
, and
M.
Lethiecq
, “
Modeling of the influence of a prestress gradient on guided wave propagation in piezoelectric structures
,”
J. Acoust. Soc. Am.
120
(
4
),
1964
1975
(
2006
).
21.
T.
Hayashi
,
W. J.
Song
, and
J. L.
Rose
, “
Guided wave dispersion curves for a bar with an arbitrary cross-section, a rod and rail example
,”
Ultrasonics
41
,
175
183
(
2003
).
22.
A.
Marzani
,
E.
Viola
,
I.
Bartoli
,
F.
Lanza di Scalea
, and
P.
Rizzo
, “
A semi-analytical finite element formulation for modeling stress wave propagation in axisymmetric damped waveguides
,”
J. Sound Vib.
318
,
488
505
(
2008
).
23.
P.
Zuo
,
X.
Yu
, and
Z.
Fan
, “
Numerical modeling of embedded solid waveguides using SAFE-PML approach using a commercially available finite element package
,”
NDT & E Int.
90
,
11
23
(
2017
).
24.
P. W.
Loveday
, “
Semi-analytical finite element analysis of elastic waveguides subjected to axial loads
,”
Ultrasonics
49
,
298
300
(
2008
).
25.
F. D.
Murnaghan
,
Finite Deformation of an Elastic Solid
(
John Wiley and Sons
,
New York
,
1951
).
26.
J. N.
Reddy
,
An Introduction to the Finite Element Method
(
McGraw-Hill
,
New York
,
1993
).
27.
L.
Wang
and
F. G.
Yuan
, “
Group velocity and characteristic wave curves of Lamb waves in composites: Modeling and experiments
,”
Compos. Sci. Technol.
67
,
1370
1384
(
2007
).
28.
M. J. S.
Lowe
, “
Matrix techniques for modeling ultrasonic waves in multilayered media
,”
IEEE Trans. Ultrason. Ferroelectr. Freq. Control
42
(
4
),
525
542
(
1995
).
29.
W. F.
Smith
and
J.
Hashemi
,
Foundations of Materials Science and Engineering
(
McGraw-Hill
,
New York
,
2010
).
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