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E-raamat: Mechanics of Elastic Waves and Ultrasonic Nondestructive Evaluation

(The University of Arizona, Tucson, USA)
  • Formaat: 396 pages
  • Ilmumisaeg: 09-Jul-2019
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9781351849395
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Mechanics of Elastic Waves and Ultrasonic Nondestructive EvaluationSuurem pilt
  • Formaat: 396 pages
  • Ilmumisaeg: 09-Jul-2019
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9781351849395
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Summary: This book presents necessary background knowledge on mechanics to understand and analyze elastic wave propagation in solids and fluids. This knowledge is necessary for elastic wave propagation modeling and for interpreting experimental data generated during ultrasonic nondestructive testing and evaluation (NDT&E). The book covers both linear and nonlinear analyses of ultrasonic NDT&E techniques. The materials presented here also include some exercise problems and solution manual. Therefore, this book can serve as a textbook or reference book for a graduate level course on elastic waves and/or ultrasonic nondestructive evaluation. It will be also useful for instructors who are interested in designing short courses on elastic wave propagation in solids or NDT&E.

The materials covered in the first two chapters provide the fundamental knowledge on linear mechanics of deformable solids while Chapter 4 covers nonlinear mechanics. Thus, both linear and nonlinear ultrasonic techniques are covered here. Nonlinear ultrasonic techniques are becoming more popular in recent years for detecting very small defects and damages. However, this topic is hardly covered in currently available textbooks. Researchers mostly rely on published research papers and research monographs to learn about nonlinear ultrasonic techniques. Chapter 3 describes elastic wave propagation modeling techniques using DPSM. Chapter 5 is dedicated to an important and very active research field acoustic source localization that is essential for structural health monitoring and for localizing crack and other type of damage initiation regions.

Features Introduces Linear and Nonlinear ultrasonic techniques in a single book. Commences with basic definitions of displacement, displacement gradient, traction and stress. Provides step by step derivations of fundamental equations of mechanics as well as linear and nonlinear wave propagation analysis. Discusses basic theory in addition to providing detailed NDE applications. Provides extensive example and exercise problems along with an extensive solutions manual.
Preface xv
Author xvii
1 Mechanics of Elastic Waves - Linear Analysis 1(112)
1.1 Fundamentals of the Continuum Mechanics and the Theory of Elasticity
1(30)
1.1.1 Deformation and Strain Tensor
1(4)
1.1.1.1 Interpretation of εij and ωij for Small Displacement Gradient
2(3)
1.1.2 Traction and Stress Tensor
5(2)
1.1.3 Traction-Stress Relation
7(1)
1.1.4 Equilibrium Equations
8(2)
1.1.4.1 Force Equilibrium
8(1)
1.1.4.2 Moment Equilibrium
9(1)
1.1.5 Stress Transformation
10(2)
1.1.5.1 Kronecker Delta Symbol (δij) and Permutation Symbol (εijk)
11(1)
1.1.6 Definition of Tensor
12(1)
1.1.7 Principal Stresses and Principal Planes
12(4)
1.1.8 Transformation of Displacement and Other Vectors
16(1)
1.1.9 Strain Transformation
16(1)
1.1.10 Definition of Elastic Material and Stress-Strain Relation
17(3)
1.1.11 Number of Independent Material Constants
20(1)
1.1.12 Material Planes of Symmetry
21(4)
1.1.12.1 One Plane of Symmetry
21(1)
1.1.12.2 Two and Three Planes of Symmetry
22(1)
1.1.12.3 Three Planes of Symmetry and One Axis of Symmetry
22(1)
1.1.12.4 Three Planes of Symmetry and Two or Three Axes of Symmetry
23(2)
1.1.13 Stress-Strain Relation for Isotropic Materials - Green's Approach
25(3)
1.1.13.1 Hooke's Law in Terms of Young's Modulus and Poisson's Ratio
27(1)
1.1.14 Navies Equation of Equilibrium
28(2)
1.1.15 Fundamental Equations of Elasticity in Other Coordinate Systems
30(1)
1.2 Time Dependent Problems or Dynamic Problems
31(63)
1.2.1 Some Simple Dynamic Problems
31(6)
1.2.2 Stokes-Helmholtz Decomposition
37(1)
1.2.3 Two-Dimensional In-Plane Problems
38(2)
1.2.4 P- and S-Waves
40(1)
1.2.5 Harmonic Waves
40(2)
1.2.6 Interaction between Plane Waves and Stress-Free Plane Boundary
42(6)
1.2.6.1 P-wave Incident on a Stress-Free Plane Boundary
42(2)
1.2.6.2 Summary of Plane P-Wave Reflection by a Stress-Free Surface
44(2)
1.2.6.3 Shear Wave Incident on a Stress-Free Plane Boundary
46(2)
1.2.7 Out-of-Plane or Antiplane Motion - SH Wave
48(4)
1.2.7.1 Interaction of SH-Wave and Stress-Free Plane Boundary
50(1)
1.2.7.2 Interaction of SH-Wave and a Plane Interface
51(1)
1.2.8 Interaction of P-and SV-Waves with Plane Interface
52(7)
1.2.8.1 P-Wave Striking an Interface
52(4)
1.2.8.2 SV-Wave Striking an Interface
56(3)
1.2.9 Rayleigh Waves in a Homogeneous Half-Space
59(4)
1.2.10 Love Wave
63(1)
1.2.11 Rayleigh Waves in a Layered Half-Space
64(2)
1.2.12 Plate Waves
66(7)
1.2.12.1 Antiplane Waves in a Plate
66(3)
1.2.12.2 In-plane Waves in a Plate (Lamb Waves)
69(4)
1.2.13 Phase Velocity and Group Velocity
73(3)
1.2.14 Point Source Excitation
76(3)
1.2.15 Wave Propagation in Fluid
79(7)
1.2.15.1 Relation between Pressure and Velocity
80(1)
1.2.15.2 Reflection and Transmission of Plane Waves at the Fluid-Fluid Interface
80(2)
1.2.15.3 Plane Wave Potential in a Fluid
82(2)
1.2.15.4 Point Source in a Fluid
84(2)
1.2.16 Reflection and Transmission of Plane Waves at a Fluid-Solid Interface
86(5)
1.2.17 Reflection and Transmission of Plane Waves by a Solid Plate Immersed in a Fluid
91(3)
1.2.18 Elastic Properties of Different Materials
94(1)
1.3 Concluding Remarks
94(6)
Exercise Problems
100(11)
References
111(2)
2 Guided Elastic Waves - Analysis and Applications in Nondestructive Evaluation 113(102)
2.1 Guided Waves and Wave-Guides
113(1)
2.1.1 Lamb Waves and Leaky Lamb Waves
114(1)
2.2 Basic Equations - Homogeneous Elastic Plates in a Vacuum
114(9)
2.2.1 Dispersion Curves and Mode Shapes
117(6)
2.2.1.1 Dispersion Curves
117(3)
2.2.1.2 Mode Shapes
120(3)
2.3 Homogeneous Elastic Plates Immersed in a Fluid
123(12)
2.3.1 Symmetric Motion
126(5)
2.3.2 Anti-Symmetric Motion
131(4)
2.4 Plane P-Waves Striking a Solid Plate Immersed in a Fluid
135(13)
2.4.1 Plate Inspection by Lamb Waves
138(10)
2.4.1.1 Generation of Multiple Lamb Modes by Narrowband and Broadband Transducers
138(2)
2.4.1.2 Nondestructive Inspection of Large Plates
140(8)
2.5 Guided Waves in Multilayered Plates
148(12)
2.5.1 n-Layered Plates in a Vacuum
148(6)
2.5.1.1 Numerical Instability
151(1)
2.5.1.2 Global Matrix Method
152(2)
2.5.2 n-Layered Plates in a Fluid
154(4)
2.5.2.1 Global Matrix Method
157(1)
2.5.3 n-Layered Plate Immersed in a Fluid, and Struck by a Plane P-Wave
158(2)
2.5.3.1 Global Matrix Method
159(1)
2.6 Guided Waves in Single and Multilayered Composite Plates
160(12)
2.6.1 Single Layer Composite Plates Immersed in a Fluid
167(1)
2.6.2 Multilayered Composite Plates Immersed in a Fluid
167(2)
2.6.3 Multilayered Composite Plates in a Vacuum (Dispersion Equation)
169(1)
2.6.4 Composite Plate Analysis with Attenuation
170(2)
2.7 Defect Detection in Multilayered Composite Plates - Experimental Investigation
172(9)
2.7.1 Specimen Description
173(1)
2.7.2 Numerical and Experimental Results
174(7)
2.8 Guided Wave Propagation in the Circumferential Direction of a Pipe
181(11)
2.8.1 Fundamental Equations
182(1)
2.8.2 Wave Form
183(1)
2.8.3 Governing Differential Equations
184(1)
2.8.4 Boundary Conditions
185(1)
2.8.5 Solution
185(2)
2.8.6 Numerical Results
187(5)
2.8.6.1 Comparison with Isotropic Flat Plate Results
187(1)
2.8.6.2 Comparison with Anisotropic Flat Plate Results
187(4)
2.8.6.3 Comparison of Results for Isotropic Pipes
191(1)
2.8.6.4 Anisotropic Pipe of Smaller Radius
191(1)
2.9 Guided Wave Propagation in the Axial Direction of a Pipe
192(13)
2.9.1 Formulation
195(5)
2.9.2 Use of Cylindrical Guided Waves for Damage Detection in Pipe wall
200(5)
2.10 Concluding Remarks
205(1)
Exercise Problems
205(3)
References
208(7)
3 Modeling Elastic Waves by Distributed Point Source Method (DPSM) 215(72)
3.1 Modeling a Finite Plane Source by a Distribution of Point Sources
215(2)
3.2 Planar Piston Transducer in a Fluid
217(17)
3.2.1 Analytical Solution
217(1)
3.2.2 Numerical Solution
218(1)
3.2.3 Semi-Analytical DPSM Solution
219(4)
3.2.4 Computed Results
223(9)
3.2.5 Required Spacing Between Neighboring Point Sources
232(2)
3.3 Focused Transducer in a Homogeneous Fluid
234(1)
3.3.1 Computed Results for a Focused Transducer
235(1)
3.4 Ultrasonic Field in a Non-Homogeneous Fluid in Presence of an Interface
235(5)
3.4.1 Field Computation in Fluid 1
236(2)
3.4.2 Field Computation in Fluid 2
238(1)
3.4.3 Satisfaction of Continuity Conditions and Evaluation of Unknowns
239(1)
3.5 Ultrasonic Field in Presence of a Scatterer
240(9)
3.5.1 DPSM Modeling
240(2)
3.5.1.1 Very Small Cavity Modeled by a Single Point Source
242(1)
3.5.12 Small Cavity Modeled with Multiple Point Sources
242(1)
3.5.1.3 Complete Solution for Large Cavity
242(1)
3.5.2 Analytical Solution
243(1)
3.5.3 Numerical Results for the Cavity Problem
244(5)
3.6 Ultrasonic Field in Multilayered Fluid Medium
249(2)
3.7 Ultrasonic Field Computation in Presence of a Fluid-Solid Interface
251(8)
3.7.1 Fluid-Solid Interface
251(2)
3.7.2 A Fluid Wedge Over a Solid Half-Space - DPSM Formulation
253(6)
3.7.3 Solid-Solid Interface
259(1)
3.8 DPSM Modeling for Transient Problems
259(9)
3.8.1 Fluid-Solid Interface Excited by a Bounded Beam - DPSM Formulation
260(8)
3.8.1.1 Transient Analysis
262(1)
3.8.1.2 Computed Results
262(6)
3.9 DPSM Modeling for Anisotropic Media
268(13)
3.9.1 DPSM Modeling of a Solid Plate Immersed in a Fluid
270(2)
3.9.2 The Windowing Technique
272(2)
3.9.3 Elastodynamic Green's Function
274(4)
3.9.3.1 General Anisotropic Materials
274(2)
3.9.3.2 Residue Method
276(1)
3.9.3.3 Reduction of Integration Domain for Transversely Isotropic Materials
277(1)
3.9.4 Numerical Examples
278(11)
3.9.4.1 Isotropic Plate
278(2)
3.9.4.2 Transversely Isotropic Plate
280(1)
3.10 Concluding Remarks
281(1)
References
282(5)
4 Nonlinear Ultrasonic Techniques for Nondestructive Evaluation 287(30)
4.1 Introduction
287(2)
4.2 One-Dimensional Analysis of Wave Propagation in a Nonlinear Material
289(10)
4.2.1 Stress-Strain Relations of Linear and Nonlinear Materials
289(1)
4.2.2 Nonlinear Material Excited by a Wave of Single Frequency
289(4)
4.2.3 Nonlinear Material Excited by Waves of Two Different Frequencies
293(1)
4.2.4 Detailed Analysis of One-Dimensional Wave Propagation in a Nonlinear Rod
294(3)
4.2.5 Higher Harmonic Generation for Other Types of Wave
297(2)
4.2.5.1 Transverse Wave Propagation in a Nonlinear Bulk Material
297(1)
4.2.5.2 Guided Wave Propagation in a Nonlinear Wave-guide
297(2)
4.3 Use of Nonlinear Bulk Waves for Nondestructive Evaluation
299(3)
4.3.1 Nonlinear Acoustic Parameter Measurement
299(1)
4.3.2 Experimental Results
300(2)
4.4 Use of Nonlinear Lamb Waves for Nondestructive Evaluation
302(3)
4.4.1 Phase Matching for Nonlinear Lamb Wave Experiments
302(1)
4.4.2 Experimental Results
303(2)
4.5 Nonlinear Resonance Technique
305(2)
4.6 Pump Wave and Probe Wave Based Technique
307(2)
4.7 Sideband Peak Count (SPC) Technique
309(4)
4.7.1 Experimental Evidence of SPC Measuring Material Nonlinearity
310(3)
4.8 Concluding Remarks
313(1)
References
314(3)
5 Acoustic Source Localization 317(54)
5.1 Introduction
317(1)
5.2 Source Localization in Isotropic Plates
318(7)
5.2.1 Triangulation Technique for Isotropic Plates with Known Wave Speed
318(2)
5.2.2 Triangulation Technique for Isotropic Plates with Unknown Wave Speed
320(1)
5.2.3 Optimization Based Technique for Isotropic Plates with Unknown Wave Speed
321(2)
5.2.4 Beamforming Technique for Isotropic Plates
323(1)
5.2.5 Strain Rossette Technique for Isotropic Plates with Unknown Wave Speed
324(1)
5.2.6 Source Localization by Modal Acoustic Emission
325(1)
5.3 Source Localization in Anisotropic Plates
325(12)
5.3.1 Beamforming Technique for Anisotropic Structure
325(1)
5.3.2 Optimization Based Technique for Source Localization in Anisotropic Plates
326(4)
5.3.3 Source Localization in Anisotropic Plates without Knowing Their Material Properties
330(4)
5.3.3.1 Determination of tij
333(1)
5.3.32 Improving and Checking the Accuracy of Prediction
334(2)
5.3.3.3 Experimental Verification
334(2)
5.3.4 Source Localization and Its Strength Estimation without Knowing the Plate Material Properties by Poynting Vector Technique
336(1)
5.4 Source Localization in Complex Structures
337(3)
5.4.1 Source Localization in Complex Structures by Time Reversal and Artificial Neural Network Techniques
338(1)
5.4.2 Source Localization by Densely Distributed Sensors
339(1)
5.5 Source Localization in Three-Dimensional Structures
340(1)
5.6 Automatic Determination of Time of Arrival
340(1)
5.7 Uncertainty in Acoustic Source Prediction
340(1)
5.8 Source Localization in Anisotropic Plates by Analyzing Propagating Wave Fronts
340(23)
5.8.1 Wave Propagation Direction Vector Measurement by Sensor Clusters
341(2)
5.8.2 Numerical Simulation of Wave Propagation in an Anisotropic Plate
343(1)
5.8.3 Wave Front Based Source Localization Technique
344(19)
5.8.3.1 Rhombus Wave Front
344(5)
5.8.3.2 Elliptical Wave Front
349(4)
5.8.3.3 Numerical Validation for Rhombus Wave Front
353(1)
5.8.3.4 Wave Front Modeled by Non-Elliptical Parametric Curve
354(4)
5.8.3.5 Numerical Validation for Non-Elliptical Wave Fronts
358(5)
5.9 Concluding Remarks
363(1)
References
364(7)
Index 371
Professor Tribikram Kundu received his bachelor degree in mechanical engineering form IIT Kharagpur, where he was the winner of the President of India Gold Medal (PGM). After completing his PhD at UCLA and winning the outstanding graduate student award he joined the faculty at the University of Arizona where he was promoted to Full Professor and was later distinguished as a Faculty Fellow in the College of Engineering. To date he has supervised 34 PhD students, published 7 books, 15 book chapters and 315 technical papers: 156 of those in refereed scientific journals. He has won the Humbolt Research Prize (Senior Scientist Award) and Humboldt Fellowship awards from Germany, 2012 NDE Life Time Achievement Award from SPIE (the International Society for Optics and Photonics), 2015 Research Award for Sustained Excellence from ASNT (American Society for Nondestructive Testing), 2015 Lifetime Achievement Award and 2008 Person of the Year Award from the Structural Health Monitoring Journal. He received a number of invited Professorships from France, Germany, Sweden, Switzerland, Spain, South Korea, Poland, China, Japan and India. He is a Fellow of 5 professional societies - ASME, ASCE, SPIE, ASNT and ASA.
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