Theory of Elastic Waves in Crystals [E-Book] / by Fedor I. Fedorov.
Fedorov, Fedor I., (author)
Boston, MA : Springer, 1968
XIII, 375 p. online resource.
englisch
9781475712759
10.1007/978-1-4757-1275-9
Full Text
Table of Contents:
  • 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.