A strip element method is presented for analyzing wave scattering by a crack in a composite laminate submerged in a fluid. In this method, the fluid and laminated plate are modeled using two-nodal-line and three-nodal-line strip elements, respectively. A system of governing equations of the fluid and solid strip elements in frequency domain are derived using a variational method and the Hamilton principle, which are converted as a set of characteristic equations in wave number domain by applying Fourier transform techniques. A particular solution to the equations is obtained using a modal analysis method in conjunction with inverse Fourier transform techniques. A complementary solution to the equations is found employing horizontal boundary conditions on cross sections at the crack tips. The addition of the particular and complementary solutions yields a general solution. Numerical examples are presented for immersed steel and composite plates with either a horizontal or a vertical crack. Computed results indicate that the fluid has considerable influence on the wave fields scattered by a crack in a composite laminate.

1.
Atalar
A.
,
1983
, “
Reflection of Ultrasonic Waves at a Liquid-Cubic-Solid Interface
,”
J. Acoust. Soc. Am.
, Vol.
73
, No.
2
, pp.
435
440
.
2.
Arikan
O.
,
Teletar
E.
, and
Atalar
A.
,
1989
, “
Reflection Coefficient Null of Acoustic Waves at a Liquid-Anisotropic-Solid Interface
,”
J. Acoust. Soc. Am.
, Vol.
85
, No.
1
, pp.
1
10
.
3.
Braga, A. M. B, and Herrmann, G., 1989, “Wave Propagation in Submerged Layered Composites,” Elastic Wave Propagation, M. F. McCarthy and M. A. Hayes, eds., Elsevier, North-Holland, Amsterdam, pp. 301–306.
4.
Chimenti
D. E.
, and
Nayfeh
A. H.
,
1990
, “
Ultrasonic Reflection and Guided Wave Propagation in Biaxially Laminated Composite Plates
,”
J. Acoust. Soc. Am.
, Vol.
87
, No.
4
, pp.
1409
1415
.
5.
Datta
S. K.
,
Ju
T. H.
, and
Shah
A. H.
,
1992
, “
Scattering of an Impact Wave by a Crack in a Composite Plate
,”
ASME JOURNAL OF APPLMD MECHANICS
, Vol.
59
, pp.
596
603
.
6.
Datta
S. K.
,
Ledbetter
H. M.
,
Shindo
Y.
, and
Shah
A. H.
,
1988
a, “
Phase Velocity and Attenuation of Plane Elastic Waves in a Particle-Reinforced Composite Medium
,”
Wave Motion
, Vol.
10
, No.
2
, pp.
171
182
.
7.
Datta
S. K.
,
Shah
A. H.
,
Bratton
R. L.
, and
Chakraborty
T.
,
1988
b, “
Wave Propagation in Laminated Composite Plates
,”
Journal of the Acoustical Society of America
, Vol.
83
, No.
6
, pp.
2020
2026
.
8.
Dayal
V.
, and
Kinra
V. K.
,
1989
, “
Leaky Lamb Waves in an Anisotropic Plate: An Exact Solution and Experiments
,”
J. Acoust. Soc. Am.
, Vol.
85
, No.
6
, pp.
2268
2276
.
9.
Gracewski
S. M.
, and
Bogy
D. B.
,
1986
, “
Elastic Wave Scattering From an Interface Crack in a Layered Half Space Submerged in Water, Part 1: Applied Tractions at the Liquid-Solid Interface; Part 2: Incident Plane Waves and Bounded Beams
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
53
, pp.
326
338
.
10.
Karim
M. R.
,
Kundu
T.
, and
Desai
C. S.
,
1989
, “
Detection of Delamination Cracks in Layered Fiber-Reinforced Composite Plates
,”
ASME Journal of Pressure Vessel Technology
, Vol.
111
, pp.
165
171
.
11.
Kundu
T.
, and
Bostro¨m
A.
,
1991
, “
Axisymmetric Scattering of a Plane Longitudinal Wave by a Circular Crack in a Transversely Isotropic Solid
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
58
, pp.
695
702
.
12.
Lam
K. Y.
,
Liu
G. R.
, and
Wang
Y. Y.
,
1997
, “
Time-Harmonic Response of a Vertical Crack in Plates
,”
Theoretical and Applied Fracture Mechanics
, Vol.
27
, pp.
21
28
.
13.
Liu
G. R.
, and
Achenbach
J. D.
,
1994
, “
A Strip Element Method for Stress Analysis of Anisotropic Linearly Elastic Solids
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
61
, pp.
270
277
.
14.
Liu
G. R.
, and
Achenbach
J. D.
,
1995
, “
Strip Element Method to Analyze Wave Scattering by Cracks in Anisotropic Laminated Plates
,”
ASME Journal of Aeplied Mechanics
, Vol.
62
, pp.
607
613
.
15.
Liu
G. R.
,
Lam
K. Y.
, and
Chan
E. S.
,
1996
, “
Stress Waves in Composite Laminates Excited by Transverse Plane Shock Waves
,”
Shock and Vibration
, Vol.
3
, No.
6
, pp.
419
433
.
16.
Liu, G. R., Wang, X. J., and Xi, Z. C., 1998, “An Exact Solution for a Wave Propagation in Composite Plate Submerged in a Fluid,” Int. J Mech. Sci., submitted for publication.
17.
Mal
A. K.
,
1988
, “
Wave Propagation in Layered Composite Laminates Under Periodic Surface Loads
,”
Wave Motion
, Vol.
10
, pp.
257
266
.
18.
Mal
A. K.
,
Xu
P. C.
, and
Bar-Cohen
Y.
,
1989
, “
Analysis of Leaky Lamb Waves in Bounded Plates
,”
Int. J. Eng. Sci.
, Vol.
27
, pp.
779
791
.
19.
Nayfeh
A. H.
,
1991
, “
Elastic Wave Reflection From Liquid-Anisotropic Substrate Interfaces
,”
Wave Motion
, Vol.
14
, No.
1
, pp.
55
67
.
20.
Nayfeh, A. H., 1995, Wave Propagation in Layered Anisotropic Media with Applications to Composites, North-Holland, Amsterdam.
21.
Nayfeh
A. H.
, and
Chimenti
D. E.
,
1988
a, “
Propagation of Guided Waves in Fluid-Coupled Plates of Fiber-Reinforced Composite
,”
J. Acoust. Soc. Am.
, Vol.
83
, No.
5
, pp.
1736
1743
.
22.
Nayfeh
A. H.
, and
Chimenti
D. E.
,
1988
b, “
Ultrasonic Wave Reflection From Liquid Coupled Orthotropic Plates With Application to Fibrous Composites
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
55
, pp.
863
870
.
23.
Nayfeh
A. H.
, and
Taylor
T. W.
,
1988
, “
Surface Wave Characteristics of Fluid Loaded Multilayered Media
,”
J. Acoust. Soc. Am.
, Vol.
84
, pp.
2187
2191
.
24.
Vinson, J. R., and Sierakowski, R. L., 1987, “The Behavior of Structures Composed of Composite Materials,” Martinus Nijhoff Publishers, Dordrecht, The Netherlands.
25.
Xi, Z. C., Liu, G. R., Lam, K. Y., and Shang, H. M., 1999, “Detection of a Crack in a Fluid-Loaded Composite Laminate,” Proceedings of the Asia-Pacific Vibration Conference ’99, DEC. 11–35, 1999, Singapore.
26.
Xi
Z. C.
,
Yam
L. H.
, and
Leung
T. P.
,
1997
a, “
Free Vibration of a Partially Fluid-Filled Cross-Ply Laminated Composite Circular Cylindrical Shell
,”
J. Acoust. Soc. Am.
, Vol.
101
, No.
3
, pp.
909
917
.
27.
Xi
Z. C.
,
Yam
L. H.
, and
Leung
T. P.
,
1997
b, “
Free Vibration of a Laminated Composite Circular Cylindrical Shell Partially Filled With Fluid
,”
Composites
, Vol.
28B
, pp.
359
375
.
This content is only available via PDF.
You do not currently have access to this content.