1.1.6 Definition of Tensor1.1.7 Principal Stresses and Principal Planes; 1.1.8 Transformation of Displacement and Other Vectors; 1.1.9 Strain Transformation; 1.1.10 Definition of Elastic Material and Stress-Strain Relation; 1.1.11 Number of Independent Material Constants; 1.1.12 Material Planes of Symmetry; 1.1.12.1 One Plane of Symmetry; 1.1.12.2 Two and Three Planes of Symmetry; 1.1.12.3 Three Planes of Symmetry and One Axis of Symmetry; 1.1.12.4 Three Planes of Symmetry and Two or Three Axes of Symmetry; 1.1.13 Stress-Strain Relation for Isotropic Materials -- Green's Approach

1.1.13.1 Hooke's Law in Terms of Young's Modulus and Poisson's Ratio1.1.14 Navier's Equation of Equilibrium; 1.1.15 Fundamental Equations of Elasticity in Other Coordinate Systems; 1.2 Time Dependent Problems or Dynamic Problems; 1.2.1 Some Simple Dynamic Problems; 1.2.2 Stokes-Helmholtz Decomposition; 1.2.3 Two-Dimensional In-Plane Problems; 1.2.4 P- and S-Waves; 1.2.5 Harmonic Waves; 1.2.6 Interaction between Plane Waves and Stress-Free Plane Boundary; 1.2.6.1 P-wave Incident on a Stress-Free Plane Boundary; 1.2.6.2 Summary of Plane P-Wave Reflection by a Stress-Free Surface

1.2.6.3 Shear Wave Incident on a Stress-Free Plane Boundary1.2.7 Out-of-Plane or Antiplane Motion -- SH Wave; 1.2.7.1 Interaction of SH-Wave and Stress-Free Plane Boundary; 1.2.7.2 Interaction of SH-Wave and a Plane Interface; 1.2.8 Interaction of P and SV-Waves with Plane Interface; 1.2.8.1 P-Wave Striking an Interface; 1.2.8.2 SV-Wave Striking an Interface; 1.2.9 Rayleigh Waves in a Homogeneous Half-Space; 1.2.10 Love Wave; 1.2.11 Rayleigh Waves in a Layered Half-Space; 1.2.12 Plate Waves; 1.2.12.1 Antiplane Waves in a Plate; 1.2.12.2 In-plane Waves in a Plate (Lamb Waves)

1.2.13 Phase Velocity and Group Velocity1.2.14 Point Source Excitation; 1.2.15 Wave Propagation in Fluid; 1.2.15.1 Relation between Pressure and Velocity; 1.2.15.2 Reflection and Transmission of Plane Waves at the Fluid-Fluid Interface; 1.2.15.3 Plane Wave Potential in a Fluid; 1.2.15.4 Point Source in a Fluid; 1.2.16 Reflection and Transmission of Plane Waves at a Fluid-Solid Interface; 1.2.17 Reflection and Transmission of Plane Waves by a Solid Plate Immersed in a Fluid; 1.2.18 Elastic Properties of Different Materials; 1.3 Concluding Remarks; Exercise Problems; References

Chapter 2 Guided Elastic Waves -- Analysis and Applications in Nondestructive Evaluation

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. FeaturesIntroduces 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.

OCLC-licensed vendor bibliographic record.