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
20 - Introduction to Guided Wave Nonlinear Methods
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
Up to this point we have described linear ultrasonics, that is, where the received signal is at the same frequency as the excitation. Now we consider nonlinear ultrasonics, where the received signal is not at the frequency of the excitation. The material is treated as weakly nonlinear elastic because the amplitude of the signal received at higher harmonics is very small relative to the excitation, which permits the use of a perturbation solution. The generation of higher harmonics in bulk solids has been studied for more than four decades, but the initial studies of higher harmonics in plates are much more recent. These studies are relevant because the amplitudes of higher harmonics have been shown to be sensitive to features of the microstructure of the material, whereas the primary harmonics are generally much less sensitive, or insensitive, to microstructural features such as dislocation density, precipitates, and cavities. This chapter introduces nonlinear methods for guided waves.
To maintain the best possible structural integrity of a component, it is highly desirable to detect damage at the smallest possible scale. Doing so with periodic nondestructive inspection or continuous structural health monitoring (SHM) enables tracking damage evolution over the service life of the structure, which can be used in conjunction with prognostics for condition-based maintenance and improved logistics. Nonlinear systems are known to be very good at indicating damage progression (e.g., Dace, Thompson, and Brashe 1991; Farrar et al. 2007; Worden et al. 2007). Generally speaking, linear ultrasonics with bulk waves can detect anomalies on the order of a wavelength. Ultrasonic guided waves can do significantly better in terms of wavelength, say λ/40 (e.g., Alleyne and Cawley 1992), but longer wavelengths are typically used to enable large penetration lengths. Nonlinear ultrasonics, where the received signal containing the information of interest is at a different frequency than the emitted signal, can provide sensitivity to microstructural changes.
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- Ultrasonic Guided Waves in Solid Media , pp. 378 - 401Publisher: Cambridge University PressPrint publication year: 2014