The practical testing of pipes in a pipe network has shown that there are issues concerning the propagation of ultrasonic guided waves through bends. It is therefore desirable to improve the understanding of the reflection and transmission characteristics of the bend. First, the dispersion curves for toroidal structures have been calculated using a finite element method, as there is no available analytical solution. Then the factors affecting the transmission and reflection behavior have been identified by studying a straight-curved-straight structure both numerically and experimentally. The frequency dependent transmission behavior obtained is explained in terms of the modes propagating in the straight and curved sections of the pipe.

1.
Rayleigh
,
L.
, 1912, “
The Problem of the Whispering Gallery
,” in
Scientific Papers
,
Cambridge University Press
, Cambridge, Vol.
5
, pp.
617
620
.
2.
Weinberg
,
H.
, and
Burridge
,
R.
, 1974, “
Horizontal Ray Theory for Ocean Acoustics
,”
J. Acoust. Soc. Am.
0001-4966,
55
, pp.
63
79
.
3.
Liu
,
G.
, and
Qu
,
J.
, 1998, “
Guided Circumferential Waves in a Circular Annulus
,”
J. Appl. Mech.
0021-8936,
65
, pp.
424
430
.
4.
Liu
,
G.
, and
Qu
,
J.
, 1998, “
Transient Wave Propagation in a Circular Annulus
,”
J. Acoust. Soc. Am.
0001-4966,
104
, pp.
1210
1220
.
5.
Wilcox
,
P.
, 1998, “
Lamb Wave Inspection of Large Structures Using Permanently Attached Transducers
,” Ph.D. thesis, University of London.
6.
Beard
,
M.
, 2002, “
Guided Wave Inspection of Embedded Cylindrical Structures
,” Ph.D. thesis, University of London.
7.
Harris
,
J.
, 2002, “
Rayleigh Wave Propagation in Curved Waveguides
,”
Wave Motion
0165-2125,
36
, pp.
425
441
.
8.
Gridin
,
D.
,
Craster
,
R. V.
,
Fong
,
J.
, and
Lowe
,
M. J. S.
, 2003, “
The High-Frequency Asymptotic Analysis of Guided Waves in a Circular Elastic Annulus
,”
Wave Motion
0165-2125,
38
, pp.
67
90
.
9.
Bretherton
,
F.
, 1968, “
Propagation in Slowly Varying Waveguides
,”
Proc. R. Soc. London, Ser. A
1364-5021,
302
, pp.
555
576
.
10.
Desaubies
,
Y.
, and
Dysthe
,
K.
, 1995, “
Normal-Mode Propagation in Slowly Varying Ocean Waveguides
,”
J. Acoust. Soc. Am.
0001-4966,
97
, pp.
933
946
.
11.
Drumheller
,
D.
, and
Knudsen
,
S.
, 1995, “
The Propagation of Sound Waves in Drill Strings
,”
J. Acoust. Soc. Am.
0001-4966,
97
, pp.
2116
2125
.
12.
Morse
,
P.
, and
Feshbach
,
H.
, 1953,
Methods of Theoretical Physics
,
McGraw-Hill
, New York.
13.
Eisenhart
,
L.
, 1934, “
Separable Systems in Euclidean 3-Space
,”
Phys. Rev.
0031-899X,
45
, pp.
427
428
.
14.
Leung
,
A.
, and
Kwok
,
N.
, 1994, “
Free Vibration Analysis of a Toroidal Shell
,”
Thin-Walled Struct.
0263-8231,
18
, pp.
317
332
.
15.
Redekop
,
M.
, 1997, “
Dynamic Response of Curved Pipes
,”
Int. J. Pressure Vessels Piping
0308-0161,
70
, pp.
167
172
.
16.
Huang
,
D.
,
Redekop
,
M.
, and
Xu
,
B.
, 1997, “
Natural Frequencies and Mode Shapes of Curved Pipes
,”
Comput. Struct.
0045-7949,
18
, pp.
465
473
.
17.
Salley
,
L.
, and
Pan
,
J.
, 2002, “
A Study of the Modal Characteristics of Curved Pipes
,”
Appl. Acoust.
0003-682X,
63
, pp.
189
202
.
18.
Gavric
,
L.
, 1995, “
Computation of Propagative Waves in Free Rail Using Finite Element Technique
,”
J. Sound Vib.
0022-460X,
185
, pp.
531
543
.
19.
Wilcox
,
P.
,
Evans
,
M.
,
Diligent
,
O.
,
Lowe
,
M.
, and
Cawley
,
P.
, 2002, “
Dispersion and Excitability of Guided Acoustic Waves in Isotropic Beams with Arbitrary Cross Section
,” in
D.
Thompson
and
D.
Chimenti
, eds.,
Review of Progress in Quantitative NDE
,
American Institute of Physics
, New York, pp.
203
210
.
20.
Pavlakovic
,
B.
,
Lowe
,
M.
,
Alleyne
,
D.
, and
Cawley
,
P.
, 1997, “
DISPERSE: A General Purpose Program for Creating Dispersion Curves
,” in
D.
Thompson
and
D.
Chimenti
, eds.,
Review of Progress in Quantitative NDE
,
Plenum
, New York, pp.
185
192
.
21.
Hitchings
,
D.
, 1994, “
FE77 User Manual
,” Technical Report,
Imperial College of Science
, Technology and Medicine, London, UK.
22.
Viktorov
,
I.
, 1965, “
Ultrasonic Lamb Waves (Review)
,”
Sov. Phys. Acoust.
0038-562X,
11
, pp.
1
14
.
23.
Pavlakovic
,
B.
, 1998, “
Leaky Guided Ultrasonic Waves in NDT
,” Ph.D. thesis, University of London.
24.
Rose
,
J.
, and
Zhao
,
X.
, 2001, “
Flexural Mode Tuning for Pipe Elbow Testing
,”
Mater. Eval.
0025-5327,
59
, pp.
621
624
.
25.
Hayashi
,
T.
, and
Rose
,
J.
, 2003, “
Guided Wave Simulation and Visualization by a Semianalytical Finite Element Method
,”
Mater. Eval.
0025-5327,
61
, pp.
75
79
.
26.
Alleyne
,
D.
,
Pavlakovic
,
B.
,
Lowe
,
M.
, and
Cawley
,
P.
, 2001, “
Rapid, Long Range Inspection of Chemical Plant Pipework Using Guided Waves
,”
Insight
1060-135X,
43
, pp.
93
96
.
27.
Cawley
,
P.
,
Alleyne
,
D.
, and
Chan
,
C.
, 1996, “
Inspection of Pipes
,” International Patent WO 96∕12951.
28.
Lowe
,
M.
,
Alleyne
,
D.
, and
Cawley
,
P.
, 1998, “
The Mode Conversion of a Guided Wave by a Part-Circumferential Notch in a Pipe
,”
J. Appl. Mech.
0021-8936,
65
, pp.
649
656
.
29.
Alleyne
,
D.
,
Lowe
,
M.
, and
Cawley
,
P.
, 1998, “
The Reflection of Guided Waves From Circumferential Notches in Pipes
,”
J. Appl. Mech.
0021-8936,
65
, pp.
635
641
.
30.
Ashwell
,
D.
, and
Gallagher
,
R.
, 1976,
Finite Elements For Thin Shells and Curved Members
,
Butterworths
, Hungary.
31.
Wang
,
R.
, 2000, “
Vibration of Straight-Curved-Straight Hollow Shafts
,”
J. Sound Vib.
0022-460X,
234
, pp.
369
386
.
32.
Aristegui
,
C.
,
Cawley
,
P.
, and
Lowe
,
M.
, 2000, “
Reflection and Mode Conversion of Guided Waves at Bends in Pipes
,” in
D.
Thompson
and
D.
Chimenti
, eds.,
Review of Progress in Quantitative NDE
,
Plenum
, New York, pp.
209
216
.
33.
Demma
,
A.
, 2003, “
The Interaction of Guided Waves with Discontinuities in Structures
,” Ph.D. thesis, University of London.
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