Elastic Wave Propagation in Transversely Isotropic Media (Paperback)

1. Basic equations.- 1. The Linearized Equations of Motion of an Anisotropic Elastic Solid.- 2. The Effect on the Equations of Motion of a Coordinate Rotation.- 3. The Elasticities for a Transversely Isotropic Solid.- 4. The Constraints on the c??'s of Positive Definiteness.- 5. The Constraints on the c??'s of Strong Ellipticity.- 6. The Uncoupled Equations of Motion in Two-Dimensions.- 7. The Uncoupled Equations of Motion in Three-Dimensions.- 8. Some Other Transversely Isotropic Continuum Theories.- 2. Wave front shape caused by a point source in unbounded media.- I Two Space Dimensions.- 1. The Characteristic Partial Differential Equation for the Wave Front.- 2. The Normal Curve.- 3. Bitangents and the Existence of Inflection Points on the Normal Curve.- 4. Bitangents Which Cross Both Coordinate Axes of the Normal Curve.- 5. Double Points of the Normal Curve.- 6. Classification of the Normal Curve Shape.- 7. Solution of the Characteristic Partial Differential Equation.- 8. Wave Front Construction as Envelope of Line Waves.- 9. Classification of the Wave Front Curve when Q is Strictly Hyperbolic.- 10. Normal and Wave Front Curves for some Hexagonal Materials.- 11. Wave Front Construction When the Normal Curve has Double Points - Convex Hull.- 12. Necessary Condition for the Existence of Wave Front Lids.- 13. The Wave Front Shape When the Normal Curve has Double Points - Conclusion.- 14. Remarks on the Wave Front Shape When the Line Load is Not Perpendicular to the Material Symmetry Axis.- II Three Space Dimensions.- 15. The Characteristic Partial Differential Equation for the Wave Front.- 16. The Normal Surface-Rotational Symmetry.- 17. Multiple Points of the Normal Surface.- 18. Wave Front Construction as Envelope of Plane Waves.- 19. The Existence of Wave Front Lids.- 20. Normal and Wave Surfaces for some Hexagonal Materials.- 3. Green's tensor for the displacement field in unbounded media.- I Two Space Dimensions.- 1. Integral Transform Representation of the Displacement Field.- 2. Transform Inversion and Reduction to a Residue Calculation.- 3. The Existence of Lacunas.- 4. Examination of the Complex p-Roots of Q(1, p, y? + z?p) = 0 When the Observation Point is on a Coordinate Axis.- 5. Displacement Components Along the Symmetry Axis for Some Hexagonal Materials.- 6. The Solution Behaviour Near the Wave Front.- 7. The Stress Field Induced by a Line Load.- 8. Remarks on the Green's Tensor Representation When the Line Load is Not Perpendicular to the Material Symmetry Axis.- II Three Space Dimensions.- 9. Integral Transform Representation of the Displacement Field.- 10. Transform Inversion for the Special Case ? = ? + ?.- 11. Transform Inversion for the General Case Along the Symmetry Axis.- 12. Application to Some Hexagonal Crystals.- 13. Herglotz-Petrowski Formula for the Displacement Field as an Integral Over the Slowness Surface.- 14. Differential Geometry of the Slowness Surface N.- 15. Remarks Concerning the Displacement Behaviour Near the Wave Front.- 4. Surface motion of a two-dimensional half-space (Lamb's problem).- 1. Formulation of the Problem.- 2. Integral Transform Representation of the Solution When the Fourier Inversion Path is Free of Branch Points.- 3. Transform Inversion for Materials Satisfying Condition (1) of Table 11.- 4. Transform Inversion for Materials Satisfying Condition (2) of Table 11.- 5. Transform Inversion for Materials Satisfying Condition (3) of Table 11.- 6. Graph of the Surface Displacements for Some Hexagonal Crystals.- 5. Epicenter and epicentral-axis motion of a three-dimensional half-space.- 1. Problem Formulation for the Epicenter Motion of a Half-Space Due to the Sudden Application of a Buried Point Source.- 2. Transform Inversion at the Epicenter for Materials Satisfying Condition (1) of Table 11.- 3. Discussion of the ?-Plane Branch Points and the Cagniard Path When the Real ?-Axis is Not Free of Branch Points.- 4. Transform Inversion at the Epicenter for Materials Satisfyin