Wave propagation across a pipe elbow region is complex. Subsequent reflected and transmitted waves are largely deformed due to mode conversions at the elbow. This prevents us to date from applying guided waves to the nondestructive evaluation of meandering pipeworks. Since theoretical development of guided wave propagation in a pipe is difficult, numerical modeling techniques are useful. We have introduced a semianalytical finite element method, a special modeling technique for guided wave propagation, because ordinary finite element methods require extremely long computational times and memory for such a long-range guided wave calculation. In this study, the semianalytical finite element method for curved pipes is developed. A curved cylindrical coordinate system is used for the curved pipe region, where a curved center axis of the pipe elbow region is an axis (z axis) of the coordinate system, instead of the straight axis (z axis) of the cylindrical coordinate system. Guided waves in the z direction are described as a superposition of orthogonal functions. The calculation region is divided only in the thickness and circumferential directions. Using this calculation technique, echoes from the back wall beyond up to four elbows are discussed.

1.
Rose
,
J. L.
, 1999,
Ultrasonic Waves in Solid Media
,
Cambridge University Press
, Cambridge.
2.
Hayashi
,
T.
, and
Endoh
,
S.
, 2000, “
Calculation and Visualization of Lamb Wave Motion
,”
Ultrasonics
0041-624X,
38
, pp.
770
773
.
3.
Hayashi
,
T.
, et al.
, “
Analysis of Flexural Mode Focusing by a Semi-Analytical Finite Element Method
,”
J. Acoust. Soc. Am.
0001-4966, (to be published).
4.
Hayashi
,
T.
, et al.
, “
Guided Wave Dispersion Curves for a Bar with an Arbitrary Cross-Section, a Rod and Rail Example
,”
Ultrasonics
0041-624X, (to be published).
5.
Heinbockel
,
J. H.
,
Introduction to Tensor Calculus and Continuum Mechanics
, Trafford.
6.
Zienkiewicz
,
O. C.
, and
Taylor
, 2000,
The Finite Element Method—Solid Mechanics
, 5th ed.,
Butterworth-Heinemann
.
7.
Liu
,
G. R.
, and
Xi
,
Z. C.
, 2001,
Elastic Waves in Anisotropic Laminates
,
CRC Press
, Boca Raton.
8.
Mudge
,
P. J.
, 2001, “
Field Application of the Teletest (R) Long-Range Ultrasonic Testing Technique
,”
Insight
1060-135X,
43
, pp.
74
77
.
You do not currently have access to this content.