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E-grāmata: Fundamentals of Ultrasonic Nondestructive Evaluation: A Modeling Approach

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Fundamentals of Ultrasonic Nondestructive Evaluation: A Modeling ApproachPalielināt
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This extensively revised and updated second edition of a widely read classic presents the use of ultrasound in nondestructive evaluation (NDE) inspections. Retaining the first edition"s use of wave propagation /scattering theory and linear system theory, this volume also adds significant new material including: the introduction of MATLAB® functions and scripts that evaluate key results involving beam propagation and scattering, flaw sizing, and the modeling of ultrasonic systems.elements of Gaussian beam theory and a multi-Gaussian ultrasonic beam model for bulk wave transducers.a new chapter on the connection between ultrasonic modeling and probability of detection (POD) and reliability models.new and improved derivations of ultrasonic measurement models.updated coverage of ultrasonic simulators that have been developed around the world. Students, engineers, and researchers working in the ultrasonic NDE field will find a wealth of information on the modeling of ultraso

nic inspections and the fundamental ultrasonic experiments that support those models in this new edition.

An Ultrasonic System.- Linear Systems and the Fourier Transform.- Fundamentals.- Propagation of Bulk Waves.- The Reciprocal Theorem and Other Integral Relations.- Reflection and Refraction of Bulk Waves.- Propagation of Surface Waves and Plate Waves.- Ultrasonic Transducer Radiation.- Material Attenuation and System Functions.- Flaw Scattering.- The Transducer Reception Process.- Ultrasonic Measurement Models.- Near Field Measurement Models.- Quantitative Ultrasonic NDE with Models.- Model-based Flaw Sizing.- Appendix A. The Fourier Transform.- Appendix B. The Dirac Delta Function.- Appendix C. Basic Notations and Concepts.- Appendix D. The Hilbert Transform.- Appendix E. The Method of Stationary Phase.- Appendix F. Properties of Ellipsoids.
1 An Ultrasonic System
1(14)
1.1 Elements of an Ultrasonic NDE System
1(2)
1.2 The Pulser-Receiver
3(2)
1.3 Ultrasonic Transducers
5(3)
1.4 Ultrasonic Digitizers
8(2)
1.5 Ultrasonic Terminology
10(2)
1.6 About the Literature
12(1)
1.7 Problems
12(3)
References
13(2)
2 Linear Systems and the Fourier Transform
15(18)
2.1 Linear Time-Shift Invariant Systems
15(1)
2.2 The Fourier Transform
16(4)
2.3 LTI Systems and the Impulse Response Function
20(2)
2.4 An Ultrasonic NDE Measurement System as an LTI System
22(4)
2.5 About the Literature
26(1)
2.6 Problems
26(7)
References
31(2)
3 Wave Motion Fundamentals
33(22)
3.1 Governing Equations for a Fluid
33(5)
3.1.1 Equations of Motion
33(1)
3.1.2 Constitutive Equations
34(2)
3.1.3 The Wave Equation
36(1)
3.1.4 Interface/Boundary Conditions
36(2)
3.2 Governing Equations for an Elastic Solid
38(13)
3.2.1 Equations of Motion
38(2)
3.2.2 Constitutive Equations
40(1)
3.2.3 Navier's Equations
41(1)
3.2.4 Interface/Boundary Conditions
42(2)
3.2.5 Wave Equations for Potentials
44(2)
3.2.6 Dilatation and Rotation
46(1)
3.2.7 Governing Equations in Cartesian Coordinates
47(4)
3.3 About the Literature
51(1)
3.4 Problems
51(4)
References
53(2)
4 Propagation of Bulk Waves
55(34)
4.1 Plane Waves in a Fluid
55(4)
4.1.1 One-Dimensional Waves
55(1)
4.1.2 Fourier Transform Relations
56(1)
4.1.3 Harmonic Waves
57(1)
4.1.4 Three-Dimensional Waves
58(1)
4.2 Plane Waves in an Elastic Solid
59(4)
4.2.1 One-Dimensional Solutions to Navier's Equations...
59(1)
4.2.2 Three-Dimensional Solutions to Navier's Equations
60(3)
4.3 Spherical Waves in a Fluid
63(6)
4.3.1 Fundamental Solution
63(3)
4.3.2 Integral Forms of the Fundamental Solution
66(2)
4.3.3 The Far Field Form of G and Its Derivatives
68(1)
4.4 Spherical Waves in an Elastic Solid
69(6)
4.4.1 Fundamental Solution
69(4)
4.4.2 The Far Field Form of Gji and its Derivatives
73(2)
4.5 Propagation of Waves in the Paraxial Approximation
75(4)
4.6 Gaussian Beams in Fluids and Elastic Solids
79(6)
4.7 About the Literature
85(1)
4.8 Problems
85(4)
References
87(2)
5 The Reciprocal Theorem and Other Integral Relations
89(24)
5.1 Reciprocal Theorem for a Fluid
89(9)
5.1.1 Integral Representation Theorem
91(1)
5.1.2 Sommerfeld Radiation Conditions
92(4)
5.1.3 Integral Equations for Scattering Problems
96(2)
5.2 Reciprocal Theorem for an Elastic Solid
98(6)
5.2.1 Integral Representation Theorem
99(2)
5.2.2 Radiation Conditions
101(2)
5.2.3 Integral Equations for Scattering Problems
103(1)
5.3 An Electromechanical Reciprocal Theorem
104(4)
5.3.1 Governing Equations
105(1)
5.3.2 The Reciprocal Theorem for a Piezoelectric Medium
106(2)
5.4 About the Literature
108(1)
5.5 Problems
108(5)
References
111(2)
6 Reflection and Transmission of Bulk Waves
113(84)
6.1 Reflection and Refraction at a Fluid-Fluid Interface (Normal Incidence)
113(7)
6.1.1 Reflection and Transmission Coefficients
114(2)
6.1.2 Acoustic Intensity of a Plane Wave
116(3)
6.1.3 Velocity Coefficients
119(1)
6.2 Reflection and Refraction at a Fluid-Fluid Interface (Oblique Incidence)
120(21)
6.2.1 Reflection and Transmission Coefficients
120(2)
6.2.2 Critical Angles and Inhomogeneous Waves
122(3)
6.2.3 Energy Reflection and Transmission: Below the Critical Angle
125(1)
6.2.4 Energy Reflection and Transmission: Above the Critical Angle
126(1)
6.2.5 Pulse Distortion
127(5)
6.2.6 Stokes' Relations
132(2)
6.2.7 Reflection and Refraction at a Fluid-Fluid Interface in Three Dimensions
134(4)
6.2.8 Snell's Law and Stationary Phase
138(3)
6.3 Reflection and Refraction at a Fluid-Solid Interface (Oblique Incidence)
141(12)
6.3.1 Reflection and Transmission Coefficients
141(7)
6.3.2 Energy Flux and Intensity for Elastic Waves
148(3)
6.3.3 Stokes' Relations (Fluid-Solid Interface)
151(2)
6.4 Reflection and Refraction at a Solid-Solid Interface (Smooth Contact)
153(4)
6.5 Reflection and Refraction at a Solid-Solid Interface (Welded Contact)
157(7)
6.5.1 Incident P- and SV-Waves
158(5)
6.5.2 Incident SH-Waves
163(1)
6.6 Reflection at a Stress-Free Surface
164(2)
6.7 Reflection, Transmission, and the Kirchhoff Approximation
166(5)
6.8 Reflection and Transmission of a Gaussian Beam at a Curved Interface
171(15)
6.8.1 Fluid-Fluid Interface
171(12)
6.8.2 Fluid-Solid and Solid-Solid Interfaces
183(3)
6.9 Snell's Law: A Discussion and Numerical Examples
186(2)
6.10 About the Literature
188(2)
6.11 Problems
190(7)
References
195(2)
7 Propagation of Surface and Plate Waves
197(22)
7.1 Rayleigh Surface Waves
197(4)
7.2 Plate Waves: Horizontal Shearing Motions
201(7)
7.3 Lamb Waves
208(7)
7.3.1 Extensional Waves
209(2)
7.3.2 Flexural Waves
211(4)
7.4 Other Waves in Bounded Media
215(1)
7.5 About the Literature
215(1)
7.6 Problems
215(4)
References
217(2)
8 Ultrasonic Transducer Radiation
219(166)
8.1 Planar Piston Transducer in a Fluid
219(32)
8.1.1 Rayleigh-Sommerfeld Theory
220(2)
8.1.2 On-Axis Pressure
222(6)
8.1.3 Off-Axis Pressure
228(19)
8.1.4 Angular Spectrum of Plane Waves and Boundary Diffraction Wave Theory
247(4)
8.2 Spherically Focused Piston Transducer in a Fluid
251(21)
8.2.1 The O'Neil Model and Others
251(3)
8.2.2 On-Axis Pressure
254(7)
8.2.3 Off-Axis Pressure
261(9)
8.2.4 Focusing by an Acoustic Lens
270(2)
8.3 Beam Propagation Through A Planar Interface: Planar Probe
272(19)
8.3.1 Fluid-Fluid Interface: Normal Incidence
272(7)
8.3.2 Fluid-Solid Interface: Normal Incidence
279(5)
8.3.3 Fluid-Fluid Interface: Oblique Incidence
284(5)
8.3.4 Fluid-Solid Interface: Oblique Incidence
289(2)
8.4 Beam Propagation Through a Planar Interface: Focused Probe
291(7)
8.4.1 Fluid-Fluid Interface
291(4)
8.4.2 Fluid-Solid Interface
295(3)
8.5 Beam Propagation Through a Curved Interface
298(25)
8.5.1 Fluid-Fluid Interface
299(18)
8.5.2 Fluid-Solid Interface
317(6)
8.6 The Numerical Evaluation of Beam Models
323(21)
8.6.1 Edge Elements
327(12)
8.6.2 Curved Interface Problems with Edge Elements
339(5)
8.7 Contact Transducer
344(8)
8.8 Angle Beam Shear Wave Transducer
352(9)
8.8.1 Angle Beam Transducer Model
352(5)
8.8.2 Edge Elements
357(4)
8.9 Multi-Gaussian Beam Models
361(14)
8.10 About the Literature
375(1)
8.11 Problems
376(9)
References
381(4)
9 Material Properties and System Function Determination
385(34)
9.1 Sources of Attenuation
386(4)
9.1.1 More Fundamental Attenuation Models
390(1)
9.2 LTI Models
390(22)
9.2.1 Diffraction Correction Integral
398(9)
9.2.2 Attenuation Measurement by Deconvolution
407(2)
9.2.3 Efficiency Factor Measurement by Deconvolution
409(3)
9.3 Wave Speed Measurements
412(1)
9.4 About the Literature
413(1)
9.5 Problems
414(5)
References
417(2)
10 Flaw Scattering
419(106)
10.1 Far Field Scattering Amplitude in a Fluid
419(3)
10.1.1 Volumetric Flaws
419(2)
10.1.2 Crack-Like Flaws
421(1)
10.2 Far Field Scattering Amplitude in an Elastic Solid
422(4)
10.2.1 Volumetric Flaws
422(3)
10.2.2 Crack-Like Flaws
425(1)
10.3 Approximate Scattering Solutions: Fluid Model
426(31)
10.3.1 The Kirchhoff Approximation: Volumetric Flaws
427(11)
10.3.2 The Kirchhoff Approximation: Cracks
438(10)
10.3.3 The Born Approximation
448(9)
10.4 Approximate Scattering Solutions: Elastic Solid Model
457(29)
10.4.1 The Kirchhoff Approximation: Volumetric Flaws
457(9)
10.4.2 The Kirchhoff Approximation: Cracks
466(11)
10.4.3 The Born Approximation
477(9)
10.5 The Far Field Scattering Amplitude and Reciprocity
486(5)
10.5.1 Scattering Amplitude in a Fluid
486(3)
10.5.2 Scattering Amplitude in an Elastic Solid
489(2)
10.6 Scattering by a Sphere: Separation of Variables
491(19)
10.6.1 Sphere in a Fluid
492(10)
10.6.2 Sphere in an Elastic Solid
502(8)
10.7 MATLAB Models
510(5)
10.8 About the Literature
515(1)
10.9 Problems
516(9)
References
521(4)
11 The Transducer Reception Process
525(14)
11.1 Reception in a Single Fluid Medium
525(2)
11.2 Reception across a Plane Fluid-Fluid Interface
527(4)
11.3 Reception across a Plane Fluid-Solid Interface
531(6)
11.4 About the Literature
537(1)
11.5 Problems
537(2)
References
537(2)
12 Ultrasonic Measurement Models
539(44)
12.1 LTI Model for a Single Fluid Medium
540(5)
12.2 LTI Model for Immersion Testing
545(7)
12.2.1 Fluid-Fluid Model
545(2)
12.2.2 Fluid-Solid Model
547(5)
12.3 Reciprocity-Based Model for Immersion Testing
552(11)
12.3.1 Auld's Model
552(7)
12.3.2 Reduction to the Thompson-Gray Model
559(4)
12.4 Reciprocity-Based Model for Contact Testing
563(7)
12.4.1 Reduction to the Thompson-Gray Model
568(2)
12.5 An Electromechanical Reciprocity-Based Measurement Model
570(3)
12.6 Measurement Models: A Discussion
573(3)
12.7 About the Literature
576(1)
12.8 Problems
577(6)
References
581(2)
13 Near Field Measurement Models
583(26)
13.1 Model for a Single Fluid Medium
583(13)
13.1.1 On-Axis Response to a Circular Transducer
589(1)
13.1.2 Scattering from a Sphere
589(3)
13.1.3 Scattering from the Flat End of a Cylinder
592(3)
13.1.4 The Paraxial Approximation Limit
595(1)
13.2 Other Models for a Single Fluid Medium
596(5)
13.3 Model for a Fluid-Solid Interface (Normal Incidence)
601(3)
13.4 About the Literature
604(1)
13.5 Problems
605(4)
References
607(2)
14 Quantitative Ultrasonic NDE with Models
609(42)
14.1 Transducer/System Characterization
610(13)
14.1.1 Effective Radius: Planar Transducer
611(1)
14.1.2 Effective Parameters: Spherically Focused Transducer
612(4)
14.1.3 System Efficiency Factor (System Function)
616(1)
14.1.4 Experimental Results
617(6)
14.2 Flat-Bottom Hole Models and DGS Diagrams
623(14)
14.2.1 Fluid-Fluid Model
631(1)
14.2.2 Special Cases
632(1)
14.2.3 DGS Diagrams
633(4)
14.3 Deconvolution and the Determination of Far Field Scattering Amplitudes
637(3)
14.4 Model-Based Ultrasonic Simulation
640(4)
14.4.1 UTSIM
640(1)
14.4.2 GPSS
641(1)
14.4.3 GB
641(1)
14.4.4 UTDefect and simSUNDT
642(1)
14.4.5 EFIT
643(1)
14.4.6 CIVA
643(1)
14.5 About the Literature
644(1)
14.6 Problems
645(6)
References
646(5)
15 Model-Based Flaw Sizing
651(34)
15.1 Concept of Equivalent Flaw Sizing
651(1)
15.2 Kirchhoff-Sizing for Cracks
652(7)
15.2.1 Nonlinear Least Squares Sizing Method
654(1)
15.2.2 Linear Least Squares/Eigenvalue Sizing Method
654(5)
15.3 Born-Sizing for Volumetric Flaws
659(7)
15.4 Time of Flight Equivalent Flaw Sizing
666(3)
15.5 Other Sizing Methods
669(6)
15.5.1 Sizing Advances and a Look to the Future of Sizing
670(5)
15.6 About the Literature
675(1)
15.7 Problems
675(10)
References
681(4)
16 Probability of Detection and Reliability
685(12)
16.1 Probability of Detection (POD) Models
685(4)
16.1.1 Noise Models
688(1)
16.1.2 Combining Model-Based and Experimental Sources of Variability
689(1)
16.2 Reliability Modeling
689(5)
16.2.1 Reliability: A Brief Overview
689(2)
16.2.2 Reliability and Inspections
691(3)
16.3 About the Literature
694(3)
References
694(3)
Appendix A The Fourier Transform 697(14)
Appendix B The Dirac Delta Function 711(4)
Appendix C Basic Notations and Concepts 715(12)
Appendix D The Hilbert Transform 727(2)
Appendix E The Method of Stationary Phase 729(8)
Appendix F Properties of Ellipsoids 737(6)
Appendix G Matlab Functions and Scripts 743(10)
Index 753
Les Schmerr received a B.S. degree in Aeronautics and Astronautics from the Massachusetts Institute of Technology in 1965 and a Ph.D. in Mechanics from the Illinois Institute of Technology in 1970. Since 1969 he has been at Iowa State University where he is currently Professor of Aerospace Engineering and Associate Director of the Center for Nondestructive Evaluation. He is also the Permanent Secretary of the World Federation of NDE Centers. His research interests include ultrasonics, elastic wave propagation and scattering, and artificial intelligence. He has developed and taught Ultrasonics and Nondestructive Evaluation courses at both the undergraduate and graduate level. He is the author of the book Fundamental of Ultrasonic Nondestructive Evaluation - A Modeling Approach which was published by Plenum Press in 1998 and the book Ultrasonic Nondestructive Evaluations Systems - Models and Measurements which was published by Springer in 2007. He is a member of IEEE, ASME, ASNT and AIAA.
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