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10 - Guided Waves in Hollow Cylinders

Published online by Cambridge University Press:  05 July 2014

Joseph L. Rose
Joseph L. Rose
Affiliation:
Pennsylvania State University
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Summary

Introduction

Ultrasonic guided waves are most commonly used in plate, rod, and hollow cylinder (pipeline and tubing) inspections. This subject is receiving much attention recently because of the possibility of inspecting long volumetric lengths of a structure from a single probe position. Components can be inspected if hidden, coated, or under insulation, oil, soil, or concrete. Excellent defect detection sensitivities and long inspection distances have been demonstrated. Guided waves in cylindrical structures may travel in the circumferential or axial direction. Based on boundary conditions, material properties, and geometric properties of the hollow cylinder, the wave behavior can be described by solving the governing wave equations with appropriate boundary conditions. In this chapter, simulations of guided waves propagating in axial directions in cylindrical structures are calculated and evaluated.

Guided Waves Propagating in an Axial Direction

In this section, a calculation approach is developed for guided wave propagation in the axial direction of a hollow cylinder.

Analytic Calculation Approach

When considering the particle motion direction possibilities in a hollow cylinder, the guided waves propagating in the axial direction may involve longitudinal waves and torsional waves. The longitudinal waves have dominant particle motions in either the r and/or z directions and the torsional waves have dominant particle motions in the direction. According to the energy distribution in the circumferential direction, the guided waves contain axisymmetric modes and non-axisymmetric modes (also known as flexural modes). For convenience, a longitudinal mode group will be expressed as L(m, n) and a torsional mode group as T(m, n). Here the integer m denotes the circumferential order of a mode and the integer n represents the group order of a mode. An axisymmetric mode has the circumferential number m = 0.

Type
Chapter
Information
Ultrasonic Guided Waves in Solid Media , pp. 155 - 173
Publisher: Cambridge University Press
Print publication year: 2014

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References

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