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Theory of Elastic Waves in Crystals

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概要 The translation into English of Academician Fedorov's ex cellent treatise on elastic wave propagation in solids has come at an opportune time. His systematic exposition of all aspects of this field is... most lucid and straightforward. The author has gone to considerable pains to develop in his mathematical background a consistent tensor framework which acts as a unifying motif through out the various aspects of the subject. In many respects his approach will appear quite novel as his treatment introduces several concepts and parameters previously unfamiliar to the literature of the West. Extensive tables in the final chapters illustrate the application of these ideas to the exist ing body of experimental data. The book is both extensive and comprehensive in al1 phases of the subject. Workers in the fields of ultrasonic propagation and elastic properties will find this treatise of great interest and direct concern. H. B. Huntington Rensselaer Polytechnic Institute Troy, New York November 1967 v Preface to the American Edition In preparing this edition I have corrected various misprints and errors appearing in the Russian edition, but I have also incorpo rated some substantial changes and additions, the latter representing some results I and my colleagues have recently obtained and pub_ lished in Russian journals. For example, in section 32 I have added a general derivation of the equation for the seetion of the wave surface by a symmetry plane for cubic, hexagonal, tetragonal, and orthorhombic crystals.続きを見る
目次 1. General Equation s of the Theory of Elasticity
1. Deformation tensor
2. Stress tensor
3. Equilibrium conditions and the equation of an elastic medium
4. Hooke's law
5. Energy of a deformed elastic body
6. Tensor for the elastic moduli
7. Crystal symmetry
8. Elastic moduli of crystals of the lower systems
9. Elastic moduli of crystals of the higher systems
2. Elements of Linear Algebra and Direct Tensor Calculus
10. Vectors and matrices in n-dimensional space.
11. Three-dimensional tensors and dyads
12. The Levi-Civita tensor and its applications
13. Eigenvalues and eigenvectors of a second-rank tensor
14. Tensor relations in a plane
3. General Laws of Propagation of Elastic Waves in Crystals
15. Plane waves and Christoffel's equation
16. General properties of the A tensor and forms of plane elastic waves in crystals
17. Special directions for elastic waves in crystals
18. Longitudinal normals and acoustic axes
19. Form of the ? tensor for various crystal systems
20. Convoluted tensor for the elastic moduli
4. Energy Flux and Wave Surfaces
21. The energy-flux vector and the ray velocity
22. Energy vector with acoustic axes
23. Elliptical polarization in elastic waves and the instantaneous energy-flux vector
24. Wave surfaces
25. Sections of the wave surfaces by symmetry planes
5. General Theory of Elastic Waves in Crystals Based on Comparison with an Isotropic Medium
26. Mean elastic anisotropy of a crystal
27. Comparison with an isotropic medium
28. Special directions
29. Approximate theory of quasilongitudinal waves
30. Another form of the approximate theory
6. Elastic Waves in Transversely Isotropic Media
31. Covariant form of the ? tensor
32. Phase velocities and displacements
33. Comparison of a hexagonal crystal with an isotropic medium
34. Mean transverse anisotropy
35. Comparison with a transversely isotropic medium
7. Elastic Waves in Crystals of the Higher Systems
36. Cubic crystals
37. Approximate theory for cubic crystals
38. Tetragonal crystals
39. Comparison with a hexagonal crystal
40. Trigonal crystals
8. Reflection and Refraction of Elastic Waves
41. Boundary conditions for plane elastic waves
42. Reflection of elastic waves at the free boundary of an isotropic medium
43. Reflection at the free boundary of a crystal
44. The complex refraction vector and inhomogeneous plane waves
45. Invariant characteristics of the polarization of plane waves
46. Inhomogeneous waves at a free boundary
9. Elastic Waves and the Thermal Capacity of a Crystal
47. Statistical theory of the thermal capacity of a solid
48. Computation of the Debye temperature
49. Averaging of the products of components of unit vector
50. Debye temperatures of cubic crystals
51. Debye temperatures of hexagonal crystals
Literature Cited.
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登録日 2020.06.27
更新日 2020.06.28