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Title: Basic Ultrasound Physics - PowerPoint PPT Presentation

1
IntroductionE Mch 521, ACS 521Stress Waves in
• Penn State University
• Instructors
• Dr. Joseph L. Rose
• Dr. Cliff Lissenden
• Textbook
• Ultrasonic Guided Waves in Solid Media
• Joseph L. Rose Cambridge University Press
2014

2
Preface
• Text Ultrasonic Waves in Solid Media, 1999
• Nondestructive Evaluation
• Structural Health Monitoring
• Growth of Guided Waves 1985 to 2014
• Publications to 2000 and beyond
• University involvement (2 to 40)
• Commercialization piping example
• ASNT working on inspection certification, a new
method
• ASME, DOT code requirements/developments

3
• Nomenclature
• Preface
• Acknowledgments
• 1. Introduction
• 1.1 Background
• 1.2 A Comparison of Bulk versus Guided Waves
• 1.3 What Is an Ultrasonic Guided Wave?
• 1.4 The Difference Between Structural Health
Monitoring (SHM) and
Nondestructive Testing (NDT)
• 1.5 Text Preview
• 1.6 Concluding Remarks
• 1.7 References

4
• 2. Dispersion Principles
• 2.1 Introduction
• 2.2 Waves in a Taut String
• 2.2.1 Governing Wave Equation
• 2.2.2 Solution by Separation of Variables
• 2.2.3 DAlemberts Solution
• 2.2.4 Initial Value Considerations
• 2.3 String on an Elastic Base
• 2.4 A Dispersive Wave Propagation Sample Problem
• 2.5 String on a Viscous Foundation
• 2.6 String on a Viscoelastic Foundation
• 2.7 Graphical Representations of a Dispersive
System
• 2.8 Group Velocity Concepts
• 2.9 Exercises
• 2.10 References

5
• 3. Unbounded Isotropic and Anisotropic Media
• 3.1 Introduction
• 3.2 Isotropic Media
• 3.2.1 Equations of Motion
• 3.2.2 Dilatational and Distortional Waves
• 3.3 The Christoffel Equation for Anisotropic
Media
• 3.3.1 Sample Problem
• 3.4 On Velocity, Wave, and Slowness Surfaces
• 3.5 Exercises
• 3.6 References

6
• 4. Reflection and Refraction
• 4.1 Introduction
• 4.2 Normal Beam Incidence Reflection Factor
• 4.3 Snells Law for Angle Beam Analysis
• 4.4 Critical Angles and Mode Conversion
• 4.5 Slowness Profiles for Refraction and
Critical Angle Analysis
• 4.6 Exercises
• 4.7 References

7
• 5. Oblique Incidence
• 5.1 Introduction
• 5.2 Reflection and Refraction Factors
• 5.2.1 Solid-Solid Boundary Conditions
• 5.2.2 Solid-Liquid Boundary Conditions
• 5.2.3 Liquid-Solid Boundary Conditions
• 5.3 Moving Forward
• 5.4 Exercises
• 5.5 References

8
• 6. Waves in Plates
• 6.1 Introduction
• 6.2 The Free Plate Problem
• 6.2.1 Solution by the Method of Potentials
• 6.2.2 The Partial Wave Technique
• 6.3 Numerical Solution of the Rayleigh-Lamb
Frequency Equations
• 6.4 Group Velocity
• 6.5 Wave Structure Analysis
• 6.6 Compressional and Flexural Waves
• 6.7 Miscellaneous Topics
• 6.7.1 Lamb Waves with Dominant Longitudinal
Displacements
• 6.7.2 Zeros and Poles for a Fluid-Coupled
Elastic Layer
• 6.7.3 Mode Cutoff Frequency
• 6.8 Exercises
• 6.9 References

9
• 7. Surface and Subsurface Waves
• 7.1 Background
• 7.2 Surface Waves
• 7.3 Generation and Reception of Surface Waves
• 7.4 Subsurface Longitudinal Waves
• 7.5 Exercises
• 7.6 References

10
• 8. Finite Element Method for Guided Wave
Mechanics
• 8.1 Introduction
• 8.2 Overview of the Finite Element Method
• 8.2.1 Using the Finite Element Method to Solve
a Problem
• 8.2.3 Dynamic Problem
• 8.2.4 Error Control
• 8.3 FEM Applications for Guided Wave Analysis
• 8.3.1 2-D Surface Wave Generation in a Plate
• 8.3.2 Guided Wave Defect Detection in a
Two-Inch Steel Tube
• 8.4 Summary
• 8.5 Exercises
• 8.6 References

11
• 9. The Semi-Analytical Finite Element Method
• 9.1 Introduction
• 9.2 SAFE Formulation for Plate Structures
• 9.3 Orthogonality-Based Mode Sorting
• 9.4 Group Velocity Dispersion Curves
• 9.5 Guided Wave Energy
• 9.5.1 Poynting Vector
• 9.5.2 Energy Velocity
• 9.5.3 Skew Effects in Anisotropic Plates
• 9.6 Solution Convergence of the SAFE Method
• 9.7 Free Guided Waves in an Eight-Layer
Quasi-Isotropic Plate
• 9.8 SAFE Formulation for Cylindrical Structures
• 9.9 Summary
• 9.10 Exercises
• 9.11 References

12
• 10. Guided Waves in Hollow Cylinders
• 10.1 Introduction
• 10.2 Guided Waves Propagating in an Axial
Direction
• 10.2.1 Analytic Calculation Approach
• 10.2.2 Excitation Conditions and Angular
Profiles
• 10.2.3 Source Influence
• 10.3 Exercises
• 10.4 References

13
• 11. Circumferential Guided Waves
• 11.1 Development of the Governing Wave Equations
for Circumferential Waves
• 11.1.1 Circumferential Shear Horizontal Waves
in a Single-Layer Annulus
• 11.1.2 Circumferential Lamb Type Waves in a
Single-Layer Annulus
• 11.2 Extension to Multiple-Layer Annuli
• 11.3 Numerical Solution of the Governing Wave
Equations for Circumferential Guided
Waves
• 11.3.1 Numerical Results for CSH-Waves
• 11.3.2 Numerical Results for CLT-Waves
• 11.3.3 Computational Limitations of the
Analytical Formulation
• 11.4 The Effects of Protective Coating on
Circumferential Wave Propagation in Pipe
• 11.5 Exercises
• 11.6 References

14
• 12. Guided Waves in Layered Structures
• 12.1 Introduction
• 12.2 Interface Waves
• 12.2.1 Waves at a Solid-Solid Interface
Stoneley Wave
• 12.2.2 Waves at a Solid-Liquid Interface
Scholte Wave
• 12.3 Waves in a Layer on a Half Space
• 12.3.1 Rayleigh-Lamb Type Waves
• 12.3.2 Love Waves
• 12.4 Waves in Multiple Layers
• 12.4.1 The Global Matrix Method
• 12.4.2 The Transfer Matrix Method
• 12.4.3 Examples
• 12.5 Fluid Couples Elastic Layers
• 12.5.1 Ultrasonic Wave Reflection and
Transmission
• 12.5.2 Leaky Guided Wave Modes
• 12.5.3 Nonspecular Reflection and Transmission
• 12.6 Exercises
• 12.7 References

15
• 13  . Source Influence on Guided Wave Excitation
• 13.1 Introduction
• 13.2 Integral Transform Method
• 13.3 Normal Mode Expansion Method
• 13.3.1 Normal Mode Expansion in Harmonic
• 13.4 Exercises
• 13.5 References

16
• 14. Horizontal Shear
• 14.1 Introduction
• 14.2 Dispersion Curves
• 14.3 Phase Velocities and Cutoff Frequencies
• 14.4 Group Velocity
• 14.5 Summary
• 14.6 Exercises
• 14.7 References

17
• 15. Guided Waves in Anisotropic Media
• 15.1 Introduction
• 15.2 Phase Velocity Dispersion
• 15.3 Guided Wave Directional Dependency
• 15.4 Guided Wave Skew Angle
• 15.5 Guided Waves in Composites with Multiple
Layers
• 15.6 Exercises
• 15.7 References

18
• 16. Guided Wave Phased Arrays in Piping
• 16.1 Introduction
• 16.2 Guided Wave Phased Array Focus Theory
• 16.3 Numerical Calculations
• 16.4 Finite Element Simulation of Guided Wave
Focusing
• 16.5 Active Focusing Experiment
• 16.6 Guided Wave Synthetic Focus
• 16.7 Synthetic Focusing Experiment
• 16.8 Summary
• 16.9 Exercises
• 16.10 References

19
• 17  . Guided Waves in Viscoelastic Media
• 17.1 Introduction
• 17.2 Viscoelastic Models
• 17.2.1 Material Viscoelastic Models
• 17.2.2 Kelvin-Voight Model
• 17.2.3 Maxwell Model
• 17.2.4 Further Aspects of the Hysteretic and
Kelvin-Voight Models
• 17.3 Measuring Viscoelastic Parameters
• 17.4 Viscoelastic Isotropic Plate
• 17.5 Viscoelastic Orthotropic Plate
• 17.5.1 Problem Formulation and Solution
• 17.5.2 Numerical Results
• 17.5.3 Summary
• 17.6 Lamb Waves in a Viscoelastic Layer
• 17.7 Viscoelastic composite Plate
• 17.8 Pipes with Viscoelastic Coatings
• 17.9 Exercises
• 17.10 References

20
• 18. Ultrasonic Vibrations
• 18.1 Introduction
• 18.2 Practical Insights into the Ultrasonic
Vibrations Problem
• 18.3 Concluding Remarks
• 18.4 Exercises
• 18.5 References

21
• 19. Guided Wave Array Transducers
• 19.1 Introduction
• 19.2 Analytical Development
• 19.2.1 Linear Comb Array Solution
• 19.2.2 Annular Array Solution
• 19.3 Phased Transducer Arrays for Mode Selection
• 19.3.1 Phased Array Analytical Development
• 19.3.2 Phased Array Analysis
• 19.4 Concluding Remarks
• 19.5 Exercises
• 19.6 References

22
• 20. Introduction to Guided Wave Nonlinear Methods
• 20.1 Introduction
• 20.2 Bulk Waves in Weakly Nonlinear Elastic
Media
• 20.3 Measurement of the Second Harmonic
• 20.4 Second Harmonic Generation Related to
Microstructure
• 20.5 Weakly Nonlinear Wave Equation
• 20.6 Higher Harmonic Generation in Plates
• 20.6.1 Synchronism
• 20.6.2 Power Flux
• 20.6.3 Group Velocity Matching
• 20.6.4 Sample Laboratory Experiments
• 20.7 Applications of Higher Harmonic Generation
by Guided Waves
• 20.8 Exercises
• 20.9 References

23
• 21. Guided Wave Imaging Methods
• 21.1 Introduction
• 21.2 Guided Wave through Transmission Dual Probe
Imaging
• 21.3 A Defect Locus Map
• 21.4 Guided Wave Tomographic Imaging
• 21.5 Guided Wave Phased Array in Plates
• 21.6 Long-Range Ultrasonic Guided Wave Pipe
Inspection Images
• 21.7 Exercises
• 21.8 References

24
Appendix A Ultrasonic Nondestructive Testing
Principles, Analysis, and Display Technology
• A.1 Physical Principles
• A.2 Wave Interference
• A.3 Computational Model for a Single Point Source
• A.4 Directivity Function for a Cylindrical
Element
• A.5 Ultrasonic Field Presentations
• A.6 Near-Field Calculations
• A.7 Angle-of-Divergence Calculations
• A.8 Ultrasonic Beam Control
• A.9 A Note of Ultrasonic Field
Solution Techniques
• A.10 Time and Frequency Domain Analysis
• A.11 Pulsed Ultrasonic Field Effects
• A.12 Introduction to Display Technology
• A.13 Amplitude Reduction of an Ultrasonic
Waveform
• A.14 Resolution and Penetration Principles
• A.14.1 Axial Resolution
• A.14.2 Lateral Resolution
• A.15 Phase Arrays and Beam Focusing
• A.16 Exercises
• A.17 References

25
• Appendix B Basic Formulas and Concepts in the
Theory of Elasticity
• B.1 Introduction
• B.2 Nomenclature
• B.3 Stress, Strain, and Constitutive Equations
• B.4 Elastic Constant Relationships
• B.5 Vector and Tensor Transformation
• B.6 Principal Stresses and Strains
• B.7 The Strain Displacement Equations
• B.8 Derivation of the Governing Wave Equation
• B.9 Anisotropic Elastic Constants
• B.10 References

26
• Appendix C Physically Based Signal Processing
Concepts for Guided Waves
• C.1 General Concepts
• C.2 The Fast Fourier Transform (FFT)
• C.2.1 Example FFT Use Analytic Envelope
• C.2.2 Example FFT Use Feature Source for
Pattern Recognition
• C.2.3 Discrete Fourier Transform Properties
• C.3 The Short Time Fourier Transform (STFFT)
• C.3.1 Example STFFT to Dispersion Curves
• C.4 The 2-D Fourier Transform (2DFFT)
• C.5 The Wavelet Transform (WT)
• C.6 Exercises
• C.7 References

27
• Appendix D Guided Wave Mode and Frequency
Selection Tips
• D.1 Introduction
• D.2 Mode and Frequency Selection Considerations
• D.2.1 A Surface-Breaking Defect
• D.2.2 Mild Corrosion and Wall Thinning
• D.2.3 Transverse Crack Detection in the Head of
a Rail
• D.2.4 Repair Patch Bonded to an Aluminum Layer
• D.2.6 Frequency and Other Tuning Possibilities
• D.2.7 Ice Detection with Ultrasonic Guided
Waves
• D.2.8 Deicing
• D.2.9 Real Time Phased Array Focusing in Pipe
• D.2.10 Aircraft, Lap-Splice, Tear Strap, and
Skin to Core Delamination Inspection
Potential
• D.2.11 Coating Delamination and Axial Crack
Detection
• D.2.12 Multilayer structures
• D.3 Exercises
• D.4 References

28
Background
• Preface
• To start now with Chapter 1. Lets see a few
references first, of many listed in the book
after each chapter.
• References
• Achenbach, J. D. (1976). Generalized continuum
theories for directionally reinforced solids,
Arch. Mech. 28(3) 25778.
• Achenbach, J. D. (1984). Wave Propagation in
Elastic Solids. New York North-Holland.
• Achenbach, J. D. (1992). Mathematical modeling
for quantitative ultrasonics, Nondestr. Test.
Eval. 8/9 36377.
• Achenbach, J. D., and Epstein, H. I. (1967).
Dynamic interaction of a layer of half space, J.
Eng. Mech. Division 5 2742.
• Achenbach, J. D., Gautesen, A. K., and McMaken,
H. (1982). Ray Methods for Waves in Elastic
Solids. Boston, MA Pitman.
• Achenbach, J. D., and Keshava, S. P. (1967). Free
waves in a plate supported by a semi-infinite
continuum, J. Appl. Mech. 34 397404.
• Auld, B. A. (1990). Acoustic Fields and Waves in
Solids. 2nd ed., vols. 1 and 2. Malabar, FL
Krieger.
• Auld, B. A., and Kino, G. S. (1971). Normal mode
theory for acoustic waves and their application
to the interdigital transducer, IEEE Trans.
ED-18 898908.

29
Background cont.
• Auld, B. A., and Tau, M. (1978). Symmetrical Lamb
wave scattering at a symmetrical pair of thin
slots, in 1977 IEEE Ultrasonic Sympos. Proc. vol.
61.
• Beranek, L. L. (1990). Acoustics. New York
Acoustical Society of America, American Institute
of Physics.
• Davies, B. (1985). Integral Transforms and Their
Applications. 2nd ed. New York Springer-Verlag.
• Eringen, A. C., and Suhubi, E. S. (1975). Linear
Theory (Elastodynamics, vol. 2). New York
• Ewing, W. M., Jardetsky, W. S., and Press, F.
(1957). Elastic Waves in Layered Media. New York
McGraw-Hill.
• Federov, F. I. (1968). Theory of Elastic Waves in
Crystals. New York Plenum.
• Graff, K. F. (1991). Wave Motion in Elastic
Solids. New York Dover.
• Kino, C. S. (1987). Acoustic Waves Devices,
Imaging and Digital Signal Processing. Englewood
Cliffs, NJ Prentice-Hall.
• Kinsler, L. E., Frey, A. R., Coppens, A. B., and
Sanders, J. V. (1982). Fundamentals of Acoustics.
New York Wiley.
• Kolsky, H. (1963). Stress Waves in Solids. New
York Dover.
• Love, A. E. H. (1926). Some Problems of
Geodynamics. Cambridge University Press.
• Love, A. E. H. (1944a). Mathematical Theory of
Elasticity. 4th ed. New York Dover.

30
Background cont.
• Love, A. E. H. (1944b). A Treatise on the
Mathematical Theory of Elasticity. New York
Dover.
• Miklowitz, J. (1978). The Theory of Elastic Waves
and Waveguides. New York North-Holland.
• Mindlin, R. D. (1955). An Introduction to the
Mathematical Theory of Vibrations of Elastic
Plates. Fort Monmouth, NJ U.S. Army Signal Corps
Engineers Laboratories.
• Musgrave, M. J. P. (1970). Crystal Acoustics. San
Francisco, CA Holden-Day.
• Pollard, H. F. (1977). Sound Waves in Solids.
London Pion Ltd.
• Rayleigh, J. W. S. (1945). The Theory of Sound.
New York Dover.
• Redwood, M. (1960). Mechanical Waveguides. New
York Pergamon.
• Rose, J. L. (1999). Ultrasonic Waves in Solid
Media. Cambridge University Press.
• Rose, J. L. (2002). A baseline and vision of
ultrasonic guided wave inspection potential,
Journal of Pressure Vessel Technology 124
27382.
• Stokes, G. G. (1876). Smiths prize examination,
Cambridge. Reprinted 1905 in Mathematics and
Physics Papers vol. 5, p. 362, Cambridge
University Press.
• Viktorov, I. A. (1967). Rayleigh and Lamb Waves
Physical Theory Applications. New York Plenum.

31
Major Contributors
• Michael Avioli
• Cody Borigo
• Jason Bostron
• Huidong Gao
• Cliff Lissenden
• Yang Liu
• Vamshi Chillara
• Jing Mu
• Jason Van Velsor
• Fei Yan
• Li Zhang

Dedication Aleksander Pilarski
32
• Wave propagation studies are not limited to NDT
and SHM, of course. Many major areas of study in
elastic wave analysis are under way, including
• (1) transient response problems, including
• (2) stress waves as a tool for studying
mechanical properties, such as the modulus of
elasticity and other anisotropic constants and
constitutive equations (the formulas relating
stress with strain and/or strain rate can be
computed from the values obtained in various,
specially designed, wave propagation
experiments)
• (3) industrial and medical ultrasonics and
acoustic-emission nondestructive testing
analysis
• (4) other creative applications, for example, in
gas entrapment determination in a pipeline, ice
detection, deicing of various structures, and
viscosity measurements of certain liquids and
• (5) ultrasonic vibration studies that combine
analysis tools in structural analysis with
high-frequency ultrasonic analysis.

33

Figure 1-1 Comparison of bulk wave and guided
wave inspection methods.
34
Table 1.1 Ultrasonic Bulk vs. Guided Wave
Propagation Considerations
BULK GUIDED
Phase Velocities Constant Function of frequency
Group Velocities Same as phase velocities Generally not equal to phase velocity
Pulse Shape Non-dispersive Generally dispersive
35
• The principal advantages of using ultrasonic
guided waves analysis techniques can be
summarized as follows.
• Inspection over long distances, as in the
length of a pipe, from a single probe position is
possible. Theres no need to scan the entire
object under consideration all of the data can
be acquired from the single probe position.
• Often, ultrasonic guided wave analysis
techniques provide greater sensitivity, and thus
a better picture of the health of the material,
than data obtained in standard localized normal
beam ultrasonic inspection or other NDT
techniques, even when using lower frequency
ultrasonic guided wave inspection techniques.
• Continued on next slide

36
• Continued from previous slide
• The ultrasonic guided wave analysis techniques
allow the inspection of hidden structures,
structures under water, coated structures,
structures running under soil, and structures
encapsulated in insulation and concrete. The
single probe position inspection using wave
structure change and wave propagation controlled
mode sensitivity over long distances makes these
techniques ideal.
• Guided wave propagation and inspection are
cost-effective because the inspection is simple
and rapid. In the example described earlier,
there would be no need to remove insulation or
coating over the length of a pipe or device
except at the location of the transducer tool.

37
Table 1.2 Ultrasonic Wave Considerations for
Isotropic vs. Anisotropic Media
ISOTROPIC ANISOTROPIC
Wave Velocities Not function of launch direction Function of launch direction
Skew Angles No Yes
38
Table 1.3 - A Comparison of the Currently Used
Ultrasonic Bulk Wave Technique and the Proposed
Ultrasonic Guided Wave Procedure for Plate and
Pipe Inspection
Bulk Wave Guided Wave
Tedious and time consuming Fast
Point by point scan (accurate rectangular grid scan) Global in nature (approximate line scan)
Unreliable (can miss points) Reliable (volumetric coverage)
High level training required for inspection Minimal training
Fixed distance from reflector required Any reasonable distance from reflector acceptable
Reflector must be accessible and seen Reflector can be hidden
39
Table 1.4. Natural Waveguides
Plates (aircraft skin)
Rods (cylindrical, square, rail, etc.)
Hollow cylinder (pipes, tubing)
Multi-layer structures
An interface
Layer or multiple layers on a half-space
40
Table 1.5. The Difference between SHM and
Non-Destructive Testing (NDT)
• SHM
• On-line evaluation
• Condition based maintenance
• Determine fitness-for-service and remaining
useful time
• Less cost and labor
• Baseline required
• Environmental data compensation methods are
required
• NDT
• Off-line evaluation
• Time base maintenance
• Find existing damage
• More cost and labor
• Baseline not available

41
Table 1.6. Successes Guided Waves in General
Increased computational efficiency developments and Understanding Basic Principles
Phased Array and Focusing developments in plates and pipes
Demonstration of optimal mode and frequency selections for penetration power, fluid loading influences, and other defect detection sensitivity requirements
42
Table 1.7 Successes Composite Materials
Understanding guided wave behavior in anisotropic media ( Slowness profiles and Skew angle influence)
Development of ultrasonic guided wave tomographic imaging methods
Comb sensor designs for optimal mode and frequency selection (linear comb and annular arrays)
43
Table 1.8 Successes Aircraft Applications
Demonstration of feasibility studies in composites and lap splice, tear strap, skin to core delamination, corrosion detection and other applications.
44
Table 1.9 Successes Pipe Inspection
Understanding and utilization of both axisymmetric and non-axisymmetric modes
Achieving excellent penetration power with special sensors, focusing, and mode and frequency choices
Defect sizing accomplishments to less than 5 cross sectional area
Reduced false alarm calls in inspection due to focusing for confirmation
Circumferential location and length of defect estimations with focusing
Testing of Pipe under insulation, coatings, and/or soil
45
Table 1.10 Practical Challenges Guided Waves in
general
Modeling accuracy is critically dependent on accurate input parameters often difficult to obtain (especially for anisotropic and viscoelastic properties, interface conditions, and defect characteristics.)
Signal interpretations often difficult (due to multimode propagation and mode conversion, along with special test structure geometric features)
Sensor robustness to environmental situations like temperature, humidity to high stress, mechanical vibrations, shock and radiation
Adhesive bonding challenges for mounting sensors and sustainability in an SHM environment
Merger of guided wave developments with energy harvesting and wireless technology
Penetration power requirements
46
Table 1.11 Practical Challenges Composite
Materials
Dealing with complex anisotropy and wave velocity and skew angle as a function of direction
Viscoelastic influences
Penetration power due to anisotropy, viscoelasticity, and inhomogeneity
Differentiating critical composite damage such as delamination defects from structural variability during fabrication (including minor fiber misalignments, ply-drops, inaccurate fiber volume fraction, and so on)
Guided wave inspection of composites with unknown material properties.
47
Table 1.12 Practical Challenges Aircraft
Applications
Robustness of guided wave sensors under in-flight conditions
Influences of aircraft paint and embedded metallic mesh in composite airframes for lightning protection
48
Table 1.13 Challenges Pipe Inspection
Tees, elbows, bends, and number of elbows and inspection beyond elbows
Quantification in defect location, characterization, sizing, especially depth determination
Inspection reliability and false alarms (due to multimode propagation, mode conversions, and so many pipe features like welds, branches, etc.)
Reducers, expanders, unknown layout drawings, cased pipes and sleeves