Book contents
- Frontmatter
- Contents
- Nomenclature
- Preface
- Acknowledgments
- 1 Introduction
- 2 Dispersion Principles
- 3 Unbounded Isotropic and Anisotropic Media
- 4 Reflection and Refraction
- 5 Oblique Incidence
- 6 Waves in Plates
- 7 Surface and Subsurface Waves
- 8 Finite Element Method for Guided Wave Mechanics
- 9 The Semi-Analytical Finite Element Method
- 10 Guided Waves in Hollow Cylinders
- 11 Circumferential Guided Waves
- 12 Guided Waves in Layered Structures
- 13 Source Influence on Guided Wave Excitation
- 14 Horizontal Shear
- 15 Guided Waves in Anisotropic Media
- 16 Guided Wave Phased Arrays in Piping
- 17 Guided Waves in Viscoelastic Media
- 18 Ultrasonic Vibrations
- 19 Guided Wave Array Transducers
- 20 Introduction to Guided Wave Nonlinear Methods
- 21 Guided Wave Imaging Methods
- Appendix A Ultrasonic Nondestructive Testing Principles, Analysis, and Display Technology
- Appendix B Basic Formulas and Concepts in the Theory of Elasticity
- Appendix C Physically Based Signal Processing Concepts for Guided Waves
- Appendix D Guided Wave Mode and Frequency Selection Tips
- Index
- Plates
- References
10 - Guided Waves in Hollow Cylinders
Published online by Cambridge University Press: 05 July 2014
- Frontmatter
- Contents
- Nomenclature
- Preface
- Acknowledgments
- 1 Introduction
- 2 Dispersion Principles
- 3 Unbounded Isotropic and Anisotropic Media
- 4 Reflection and Refraction
- 5 Oblique Incidence
- 6 Waves in Plates
- 7 Surface and Subsurface Waves
- 8 Finite Element Method for Guided Wave Mechanics
- 9 The Semi-Analytical Finite Element Method
- 10 Guided Waves in Hollow Cylinders
- 11 Circumferential Guided Waves
- 12 Guided Waves in Layered Structures
- 13 Source Influence on Guided Wave Excitation
- 14 Horizontal Shear
- 15 Guided Waves in Anisotropic Media
- 16 Guided Wave Phased Arrays in Piping
- 17 Guided Waves in Viscoelastic Media
- 18 Ultrasonic Vibrations
- 19 Guided Wave Array Transducers
- 20 Introduction to Guided Wave Nonlinear Methods
- 21 Guided Wave Imaging Methods
- Appendix A Ultrasonic Nondestructive Testing Principles, Analysis, and Display Technology
- Appendix B Basic Formulas and Concepts in the Theory of Elasticity
- Appendix C Physically Based Signal Processing Concepts for Guided Waves
- Appendix D Guided Wave Mode and Frequency Selection Tips
- Index
- Plates
- References
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.
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- Information
- Ultrasonic Guided Waves in Solid Media , pp. 155 - 173Publisher: Cambridge University PressPrint publication year: 2014
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