A Study on Scattered Wave Amplitude Closed-Form Solution Calculation of Torsional Wave Mode by Reciprocity Theorem

- Journal title : Transactions of the Korean Society of Mechanical Engineers A
- Volume 40, Issue 7, 2016, pp.647-652
- Publisher : The Korean Society of Mechanical Engineers
- DOI : 10.3795/KSME-A.2016.40.7.647

Title & Authors

A Study on Scattered Wave Amplitude Closed-Form Solution Calculation of Torsional Wave Mode by Reciprocity Theorem

Lee, Jaesun; Cho, Younho; Achenbach, Jan D.;

Lee, Jaesun; Cho, Younho; Achenbach, Jan D.;

Abstract

Guided waves can be used for the inspection of long range pipelines. Surface corrosion is often found as a major defect type in pipelines. The reciprocity relation is a well-established theorem by which one can simplify complicated mathematical expressions. The approach has been already applied to plate and half-space structures to obtain the closed-form solutions of scattered amplitude. However, results for the case of cylindrical structures have not been reported yet. In this paper, the scattering of torsional waves, which is widely used in commercial applications, is explored by the reciprocity theorem approach. Obtaining closed-form solutions of the amplitudes of propagating waves is much simplified by using the reciprocal relation. The scattered amplitudes for elliptical and rectangular defect shapes are calculated with respect to defect depth and width, at frequencies between 0 and 500 kHz. The amplitude shows the periodic result as a function of frequency. The derived closed-form solutions can play a significant role in quantitative signal interpretation.

Keywords

Guided Wave;Reciprocity Theorem;Torsional Wave Mode;Corrosion;Scattered Wave;Closed Form Solution;

Language

Korean

References

1.

Lee, J., Cho, Y. and Jeong, K., 2009, "Material Characterization of Lock Plate Using Guided Wave," Trans. Korean Soc. Mech. Eng. A, Vol. 33, No. 4, pp. 373-379.

2.

Cho, Y., Jung, K. and Lee, J., 2010, "Use of Guided Waves for Monitoring Material Conditions in Fossil-Fuel Power Plants," Trans Korean Soc. Mech. Eng. A, Vol. 34, No. 6, pp. 695-700.

3.

Alleyne, D. N. and Cawley, P., 1992, "The Interaction of Lamb Waves with Defects," Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on, Vol. 39, No. 3, pp. 381-397.

4.

Rose, J., Ditri, J. J., Pilarski, A., Rajana, K. and Carr, F., 1994, "A Guided Wave Inspection Technique for Nuclear Steam Generator Tubing," NDT & E International, Vol. 27, No. 6, pp. 307-310.

5.

Rose, J. L., Jiao, D. and Spanner Jr, J., 1996, "Ultrasonic Guided Wave NDE for Piping," Materials Evaluation, Vol. 54, No. 11, pp. 1310-1313.

6.

Lowe, M. J., Alleyne, D. N. and Cawley, P., 1998, "Defect Detection in Pipes Using Guided Waves," Ultrasonics, Vol. 36, No. 1, pp. 147-154.

7.

Shin, H. J. and Rose, J. L., 1998, "Guided Wave Tuning Principles for Defect Detection in Tubing," Journal of nondestructive evaluation, Vol. 17, No. 1, pp. 27-36.

8.

Demma, A., Cawley, P., Lowe, M. and Roosenbrand, A., 2003, "The Reflection of the Fundamental Torsional Mode From Cracks and Notches in Pipes," The Journal of the Acoustical Society of America, Vol. 114, No. 2, pp. 611-625.

9.

Demma, A., Cawley, P., Lowe, M., Roosenbrand, A. and Pavlakovic, B., 2004, "The Reflection of Guided Waves From Notches in Pipes: a Guide for Interpreting Corrosion Measurements," Ndt & E International, Vol. 37, No. 3, pp. 167-180.

10.

Carandente, R., Ma, J. and Cawley, P., 2010, "The Scattering of the Fundamental Torsional Mode from Axi-symmetric Defects with Varying Depth Profile in Pipes," The Journal of the Acoustical Society of America, Vol. 127, No. 6, pp. 3440-3448.

11.

Ratassepp, M., Fletcher, S. and Lowe, M., 2010, "Scattering of the Fundamental Torsional Mode at an Axial Crack in a Pipe," The Journal of the Acoustical Society of America, Vol. 127, No. 2, pp. 730-740.

12.

Achenbach, J. D., 2003, Reciprocity in Elastodynamics, Cambridge University Press, pp. 55-115.

13.

Achenbach, J., 2000, "Calculation of Surface Wave Motions Due to a Subsurface Point Force: An Application of Elastodynamic Reciprocity," The Journal of the Acoustical Society of America, Vol. 107, No. 4, pp. 1892-1897.

14.

Achenbach, J., 2005, "Combination of a Virtual Wave and the Reciprocity Theorem to Analyse Surface Wave Generation on a Transversely Isotropic Solid," Philosophical Magazine, Vol. 85, No. 33-35, pp. 4143-4157.