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RESEARCH PAPERS

A Guided Wave Plate Experiment for a Pipe

[+] Author and Article Information
Wei Luo, Joseph L. Rose

Department of Engineering Science & Mechanics, The Pennsylvania State University, University Park, PA 16802

Xiaoliang Zhao

 Intelligent Automation, Inc., 15400 Calhoun Dr., Suite 400, Rockville, MD 20855

J. Pressure Vessel Technol 127(3), 345-350 (Mar 04, 2005) (6 pages) doi:10.1115/1.1989351 History: Received January 17, 2005; Revised March 04, 2005

The plate approximation of a pipe is a topic discussed for decades. Rules have been established to make the comparisons. Presented here is a related topic, but one to answer the question of whether an easy-to-conduct plate experiment can be used to predict what happens in a pipe for ultrasonic guided wave. For longitudinal guided waves in a pipe, the approximation is valid clearly only over a very short distance or inordinate closeness to a defect for wave scattering analysis; but for circumferential guided waves, the validity is unclear and therefore it is worthwhile to study criteria on the approximation and simplification of a pipe experiment as a plate experiment by means of wave mechanics analysis and modeling computation. Circumferential shear horizontal (SH) waves in pipes and SH waves in plates were studied in this paper toward this goal and it was found that the wave frequency and wall thickness to radius ratio were the two key parameters with respect to the similarity. Dispersion curves and wave structures of the SH waves in plates and in pipes were compared to find the origin of the similarity. Experimental simulations and modeling with boundary element methods were also carried out for the reflection and transmission coefficients of the SH waves impinging into a defect, from which some criteria have been established for the plate model approximation. Although a pipe model is more accurate for pipe experiments, a plate model often gives a quick and reasonable solution especially when it is difficult to establish a pipe model.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

Phase velocity dispersion curve for circumferential SH waves of a hollow cylinder, compared with the dispersion curves for SH waves in a plate with the same thickness. In the legend, d is the wall thickness and R is the outer radius of the cylinder.

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Figure 2

Lateral displacement wave structures of 10 mm wall pipes with different d∕R 20%, 50%, 80%, for circumferential n0 mode SH wave and fd=1MHzmm, compared with the wave structure of a plate with the same thickness for n0 mode SH wave and fd=1MHzmm

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Figure 3

Constant boundary element mesh for evaluating guided wave scattering from a surface-breaking defect

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Figure 4

Boundary element mesh for evaluating circumferential SH guided wave scattering in a pipe

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Figure 5

Calculated reflection factors for n0 mode under n0 incidence onto a 0.3 mm notch with 50% through-pipe-wall depth for pipes of 10 mm thickness and various thickness-over-outer-radius ratios 5%,10%,…,60%, compared with the reflection factors for a 10 mm steel plate

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Figure 6

Errors of reflection factors for the pipes ∣R∣pi compared with the reflection factors ∣R∣pl for the plate (for 50% through-wall depth)

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Figure 7

Calculated transmission factors for n0 mode under n0 incidence onto a 0.3 mm notch with 50% through-pipe-wall depth for pipes of 10 mm thickness and various thickness-over-outer-radius ratios 5%,10%,…,60%, compared with the transmission factors for a 10 mm steel plate

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Figure 8

Errors of transmission factors ∣T∣pi for pipes compared with the transmission factors ∣T∣pl for the plate (for 50% through-wall depth)

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Figure 9

Critical d∕R values under which reflection or transmission factor errors between the pipe and the plate are less than 5% (for 50% through-wall depth)

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Figure 10

Critical d∕R values under which both transmission and reflection factor errors between the pipe and the plate are less than 5% (for 50% through-wall depth). This is realized by selecting the minimal critical d∕R values from the two curves in Fig. 9.

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Figure 11

Critical d∕R values under which both transmission and reflection factor errors between the pipe and the plate are less than 5%, for 10%,30%,…, and 90% through-wall depths

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Figure 12

The minimal and average critical d∕R values for 10%, 30%,…, 90% through-wall depths, under which both transmission and reflection factor errors between the pipe and the plate are less than 5%

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