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Table of Contents
Intro
Acknowledgments
Author biography
Cliff J Lissenden
Chapter Introduction
1.1 Motivation
1.2 Brief perspective on nonlinear ultrasonic guided waves
1.3 Approach
1.4 Content
1.5 Closure
References
Chapter Preliminaries
2.1 Notation
2.2 Continuum mechanics
2.2.1 Kinematics
Example 2.2. Normal strains
Example 2.3. Shear strain
2.2.2 Balance laws
2.2.3 Stress
2.2.4 Constitutive relations
Example 2.4. Stress components decomposed into linear and nonlinear parts
Example 2.5. Strain energy function for transversely isotropic material
2.3 Elastodynamics
2.3.1 Wave equation
2.3.2 Wave equation for isotropic materials
2.3.3 Attenuation
2.4 Closure
References
Chapter Nonlinear elastic waves
3.1 Bulk longitudinal waves
Example 3.1. Longitudinal wave nonlinearity
Example 3.2. Regular perturbation approach to the nonlinear longitudinal wave problem
Example 3.3. Nonlinear longitudinal wave solution using the method of multiple scales
Example 3.4. Determine β in terms of Landau-Lifshitz TOECs for an isotropic material
3.2 Bulk shear waves
Example 3.5. Shear wave third harmonic generation
3.3 Attenuation
3.4 Measurements of nonlinearity
3.4.1 Acoustoelasticity
3.4.2 Second harmonic generation
3.4.3 Wave mixing
3.4.4 Nonlinear resonant ultrasound spectroscopy (NRUS)
3.4.5 Vibro-acoustics
3.4.6 Dynamic acoustoelastic testing
3.5 Closure
References
Chapter Boundary value problem formulation
4.1 Linear BVPs
4.1.1 Free surfaces
4.1.2 Plates
4.1.3 Hollow cylinders
4.1.4 Arbitrary cross-sections
4.2 Nonlinear BVPs
4.2.1 Regular perturbation method
4.2.2 Wave interactions
Example 4.1. Third order interactions
4.3 Closure
References
Chapter Ultrasonic guided waves-linear features.
5.1 Physical characteristics of waves
5.1.1 Phase velocity
5.1.2 Wavestructure
5.1.3 Group velocity
Example 5.1. Group velocity calculation
5.1.4 Attenuation
5.2 Rayleigh waves
5.3 Waves in plates
5.3.1 Shear-horizontal (SH) waves
5.3.2 Lamb waves
5.3.3 Anisotropic plates
5.3.4 Finite-width plates
5.4 Hollow cylinder waves
5.5 Other types of guided waves
5.6 Closure
References
Chapter Nonlinear analysis of plates
6.1 Reciprocity
6.2 Orthogonality
Example 6.1. Auld's real reciprocity relation
Example 6.2. Orthogonality of SH waves
Example 6.3. Orthogonality of Lamb waves
6.3 Completeness
6.4 Normal mode expansion
6.5 Perturbation approach
6.6 Internal resonance
Example 6.4. Second harmonic generation of Lamb waves
6.7 Wave mixing
6.8 Closure
References
Chapter Internal resonance in plates
7.1 Power flow for self-interaction
7.1.1 Second order
7.1.2 Third order
7.2 Power flow for mutual interaction
7.2.1 Second order co-directional
Example 7.1. Parity analysis of mutual interaction between SRL and ASH wavefields
7.2.2 Third order co-directional
7.3 Effect of directionality
7.4 Synchronism
7.4.1 Second order self-interaction
7.4.2 Third order self-interaction
7.5 Group velocity matching
7.5.1 Co-directional wave mixing
7.5.2 Counter-propagating wave mixing
7.5.3 Non-collinear wave mixing
7.6 Comments on hollow cylinders
7.7 Closure
References
Chapter Selecting primary waves
8.1 Self-interaction in plates
8.1.1 Seond harmonic generation
8.1.2 Third harmonic generation
8.1.3 Method of multiple scales
8.2 Mutual interaction in plates
8.2.1 Co-directional, θ=0°
8.2.2 Counter-propagating, θ=180°
8.2.3 Non-collinear, θτ̔̈““ «·0° and θτ̔̈““ «·180°
8.3 Hollow cylinders
8.4 Arbitrary cross-section.
8.5 Half-space
8.6 Closure
References
Chapter Finite amplitude pulse loading
9.1 Descriptors of nonlinearity
9.2 Experimental results from laser generation
Example 9.1 Relationship between Rayleigh wave components
9.3 Modeling waveform evolution
9.4 Closure
References
Chapter Numerical simulations
10.1 Methods
10.2 Software tools
10.3 Sample problems
10.3.1 Reported in the literature
10.3.2 Lamb wave analyses using commercial software
10.4 Closure
References
Chapter Making measurements
11.1 Instrumentation
11.2 Generation
11.2.1 Transmitting transducers
11.2.2 Transmitting methods
11.3 Reception
11.3.1 Receiving transducers
11.3.2 Receiving methods
11.4 Signal processing
11.5 Closure
References
Chapter Highlights of experimental testing
12.1 Self-interaction
12.2 Mutual interaction
12.3 Quasi-Rayleigh waves
12.4 Closure
References
Chapter Perspective
13.1 Separation of material nonlinearity from measurement system nonlinearity
13.2 Link with the structural design that identifies hot spots to be monitored and a plan for inclusion of nonlinear ultrasonic guided waves in the operations management and maintenance planning
13.3 Standards for test methods that are broad enough to be applicable to the emerging needs for offline inspection and in-service monitoring
13.4 Define specifications needed to build monitoring systems into self-aware smart structures
13.5 Solid connection between nonlinear wave propagation characteristics and the material microstructure that dictates its strength and fracture properties
References.
Acknowledgments
Author biography
Cliff J Lissenden
Chapter Introduction
1.1 Motivation
1.2 Brief perspective on nonlinear ultrasonic guided waves
1.3 Approach
1.4 Content
1.5 Closure
References
Chapter Preliminaries
2.1 Notation
2.2 Continuum mechanics
2.2.1 Kinematics
Example 2.2. Normal strains
Example 2.3. Shear strain
2.2.2 Balance laws
2.2.3 Stress
2.2.4 Constitutive relations
Example 2.4. Stress components decomposed into linear and nonlinear parts
Example 2.5. Strain energy function for transversely isotropic material
2.3 Elastodynamics
2.3.1 Wave equation
2.3.2 Wave equation for isotropic materials
2.3.3 Attenuation
2.4 Closure
References
Chapter Nonlinear elastic waves
3.1 Bulk longitudinal waves
Example 3.1. Longitudinal wave nonlinearity
Example 3.2. Regular perturbation approach to the nonlinear longitudinal wave problem
Example 3.3. Nonlinear longitudinal wave solution using the method of multiple scales
Example 3.4. Determine β in terms of Landau-Lifshitz TOECs for an isotropic material
3.2 Bulk shear waves
Example 3.5. Shear wave third harmonic generation
3.3 Attenuation
3.4 Measurements of nonlinearity
3.4.1 Acoustoelasticity
3.4.2 Second harmonic generation
3.4.3 Wave mixing
3.4.4 Nonlinear resonant ultrasound spectroscopy (NRUS)
3.4.5 Vibro-acoustics
3.4.6 Dynamic acoustoelastic testing
3.5 Closure
References
Chapter Boundary value problem formulation
4.1 Linear BVPs
4.1.1 Free surfaces
4.1.2 Plates
4.1.3 Hollow cylinders
4.1.4 Arbitrary cross-sections
4.2 Nonlinear BVPs
4.2.1 Regular perturbation method
4.2.2 Wave interactions
Example 4.1. Third order interactions
4.3 Closure
References
Chapter Ultrasonic guided waves-linear features.
5.1 Physical characteristics of waves
5.1.1 Phase velocity
5.1.2 Wavestructure
5.1.3 Group velocity
Example 5.1. Group velocity calculation
5.1.4 Attenuation
5.2 Rayleigh waves
5.3 Waves in plates
5.3.1 Shear-horizontal (SH) waves
5.3.2 Lamb waves
5.3.3 Anisotropic plates
5.3.4 Finite-width plates
5.4 Hollow cylinder waves
5.5 Other types of guided waves
5.6 Closure
References
Chapter Nonlinear analysis of plates
6.1 Reciprocity
6.2 Orthogonality
Example 6.1. Auld's real reciprocity relation
Example 6.2. Orthogonality of SH waves
Example 6.3. Orthogonality of Lamb waves
6.3 Completeness
6.4 Normal mode expansion
6.5 Perturbation approach
6.6 Internal resonance
Example 6.4. Second harmonic generation of Lamb waves
6.7 Wave mixing
6.8 Closure
References
Chapter Internal resonance in plates
7.1 Power flow for self-interaction
7.1.1 Second order
7.1.2 Third order
7.2 Power flow for mutual interaction
7.2.1 Second order co-directional
Example 7.1. Parity analysis of mutual interaction between SRL and ASH wavefields
7.2.2 Third order co-directional
7.3 Effect of directionality
7.4 Synchronism
7.4.1 Second order self-interaction
7.4.2 Third order self-interaction
7.5 Group velocity matching
7.5.1 Co-directional wave mixing
7.5.2 Counter-propagating wave mixing
7.5.3 Non-collinear wave mixing
7.6 Comments on hollow cylinders
7.7 Closure
References
Chapter Selecting primary waves
8.1 Self-interaction in plates
8.1.1 Seond harmonic generation
8.1.2 Third harmonic generation
8.1.3 Method of multiple scales
8.2 Mutual interaction in plates
8.2.1 Co-directional, θ=0°
8.2.2 Counter-propagating, θ=180°
8.2.3 Non-collinear, θτ̔̈““ «·0° and θτ̔̈““ «·180°
8.3 Hollow cylinders
8.4 Arbitrary cross-section.
8.5 Half-space
8.6 Closure
References
Chapter Finite amplitude pulse loading
9.1 Descriptors of nonlinearity
9.2 Experimental results from laser generation
Example 9.1 Relationship between Rayleigh wave components
9.3 Modeling waveform evolution
9.4 Closure
References
Chapter Numerical simulations
10.1 Methods
10.2 Software tools
10.3 Sample problems
10.3.1 Reported in the literature
10.3.2 Lamb wave analyses using commercial software
10.4 Closure
References
Chapter Making measurements
11.1 Instrumentation
11.2 Generation
11.2.1 Transmitting transducers
11.2.2 Transmitting methods
11.3 Reception
11.3.1 Receiving transducers
11.3.2 Receiving methods
11.4 Signal processing
11.5 Closure
References
Chapter Highlights of experimental testing
12.1 Self-interaction
12.2 Mutual interaction
12.3 Quasi-Rayleigh waves
12.4 Closure
References
Chapter Perspective
13.1 Separation of material nonlinearity from measurement system nonlinearity
13.2 Link with the structural design that identifies hot spots to be monitored and a plan for inclusion of nonlinear ultrasonic guided waves in the operations management and maintenance planning
13.3 Standards for test methods that are broad enough to be applicable to the emerging needs for offline inspection and in-service monitoring
13.4 Define specifications needed to build monitoring systems into self-aware smart structures
13.5 Solid connection between nonlinear wave propagation characteristics and the material microstructure that dictates its strength and fracture properties
References.