Linear Theory

PrefaceAcknowledgmentsContents of Volume IChapter V. Fundamentals of Linear Elastodynamics 5.1 Scope of the Chapter 5.2 Resume of Basic Equations of Linear Elasticity 5.3 Displacement Formulation of Elastodynamics 5.4 Displacement Potentials 5.5 Stress Formulation of Elastodynamics 5.6 Convoluted Forms of the Field Equations 5.7 Uniqueness Theorem of Elastodynamics 5.8 Reciprocal Theorem 5.9 Some Properties of the Wave Equation 5.10 Fundamental Singular Solution of Elastodynamics 5.11 Integral Representation Theorems 5.12 Two-Dimensional Representation Theorem 5.13 Radiation Conditions 5.14 Integral Equation Formulation of Boundary-Value Problems 5.15 Green's Functions of Elastodynamic States 5.16 Reduced Elastodynamic Equations 5.17 Solution of Elastodynamic Equations by Eigenfunction Expansions 5.18 Variational Principles for Linear Elastodynamics Chapter VI. One-Dimensional Motions 6.1 Scope of the Chapter 6.2 One-Dimensional Elastodynamic Equations 6.3 D'Alembert Solution 6.4 Propagation of Longitudinal Waves in Half-Space 6.5 Initial-Value Problem for a Finite Strip 6.6 Finite Strip Fixed at One End and Subject to Dynamical Tractions at the Other 6.7 Propagation of Spherical Waves 6.8 Spherical Cavity Subject to Dynamical Pressure 6.9 Eigenfunctions for Spherical Domains 6.10 Propagation of Cylindrical Waves 6.11 Cylindrical Cavity Subject to Dynamical Pressure 6.12 Eigenfunctions for Cylindrical Domains 6.13 Initial-Value Problem for Cylindrical WavesChapter VII. Two-Dimensional Motions 7.1 Scope of the Chapter 7.2 Fundamental Equations 7.3 Lame Potentials 7.4 Propagation of Plane Harmonic Waves 7.5 Plane Elastic Waves in a Half-Space with a Free Boundary 7.6 Harmonic Surface Waves on a Half-Space 7.7 Waves in Layered Media 7.8 Dispersion and Group Velocity 7.9 Elastic Waves in Infinite Plates 7.10 Solutions by Complex Functions 7.11 Moving Line Load on the Surface of a Half-Space 7.12 Moving Griffith Crack 7.13 Moving Punch on a Half-Space 7.14 Self-Similar Solutions of Plane Problems 7.15 Similarity Solutions for the Half-Space 7.16 Line Impulse on the Surface of a Half-Space 7.17 Miscellaneous Stress Boundary-Value Problems in Half-Space 7.18 A Dynamic Contact Problem in Half-Space 7.19 Some Remarks-Other Solutions 7.20 Integral Transform Methods 7.21 Lamb's Problem 7.22 Transient Solution of the Problem of Buried Pressure Line Source in Half-Space 7.23 Impulsive Buried Line Force 7.24 Transient Motion of a Surface Line Load 7.25 Infinite Slab under Surface Loads 7.26 Antiplane Motion of a Slab Subject to End Loads 7.27 Plane-Strain Vibrations of Circular Cylinders 7.28 Circular Cylinder Subjected to Dynamical Tractions 7.29 Dynamic Tractions in a Circular CavityChapter VIII. Three-Dimensional Solutions 8.1 Scope of the Chapter 8.2 Basic Equations in Curvilinear Coordinates 8.3 Infinite Elastic Space Subjected to Dynamical Loads 8.4 Finite Line Source in Infinite Elastic Space 8.5 Half-Space Subjected to Surface Twist 8.6 Lamb's Problem 8.7 Half-Space under Moving Load 8.8 Self-Similar Solutions of Axisymmetric Problems 8.9 The Circular Cylinder Problem 8.10 Vibrations of a Circular Cylinder 8.11 Propagation of Waves in a Hollow Circular Cylinder 8.12 Infinite Cylinder under Surface Tractions 8.13 The Sphere Problem 8.14 Free Vibrations of an Elastic Sphere 8.15 Elastic Sphere and Spherical Cavity Subjected to Dynamical Surface Loads 8.16 Torsion of Sphere 8.17 Elastic Sphere under Polar Traction 8.18 Incompressible Elastic SphereChapter IX. Diffraction of Elastic Waves 9.1 Scope of the Chapter 9.2 Methods of Solution 9.3 Scattering of SH-Waves by a Rigid Cylinder 9.