Читать книгу Elastic Waves in Solids 1 - Daniel Royer - Страница 3

1 Chapter 1Figure 1.1. Equilibrium of a fixed volume V inside the solidFigure 1.2. Three stresses act on each of the three orthogonal faces. From the p...Figure 1.3. At any point M marked by the vector <u>x</u>, the vibration created ...Figure 1.4. a) Longitudinal wave: polarization and wave vector are parallel. At ...Figure 1.5. Cylindrical waves: a) longitudinal and b) transverseFigure 1.6. Composite made up of carbon fibers embedded in a thermoset epoxy res...Figure 1.7. In general, three plane waves propagate in any direction <u>n</u> of...Figure 1.8. The propagation direction n is defined by the angles θ and ϕFigure 1.9. Propagation in the symmetry plane XY of an orthotropic solid. The qu...Figure 1.10. The projection of the energy velocity vector <u>V</u>e on the propa...Figure 1.11. Characteristic surfaces: a) Slowness surface: the energy velocity <...Figure 1.12. Section of the wave surface. A change in curvature of the slowness ...Figure 1.13. a) Slowness surface (s/km) and b) wave surface for a copper crystal...Figure 1.14. Cross-section of (a) the slowness surface and (b) the wave surface ...Figure 1.15. 3D slowness surface of quasi-longitudinal and quasi-transverse wave...Figure 1.16. Slowness curves (s/km) in the XY plane for bismuth germanium oxide....Figure 1.17. Cross-section of the slowness surface of lithium niobate (class 3m)...Figure 1.18. Electromechanical coupling coefficients KL and KT as functions of t...Figure 1.19. Maxwell model. The real and imaginary components of an elastic modu...Figure 1.20. Imaginary component of the shear modulus of a polymer as a function...

2 Chapter 2Figure 2.1. If the density of the force p exerted on the surface Σ is zer...Figure 2.2. Snell–Descartes law. The projections, on the interface between the t...Figure 2.3. Interface between two isotropic solids. The incident transverse vert...Figure 2.4. Isotropic solid: Reflection of an incident wave that is a) transvers...Figure 2.5. Diagram of the successive echoes in the plateFigure 2.6. Evolution of the moduli of the reflection (r) and transmission (t) c...Figure 2.7. Moduli of the reflection coefficients a) rLL and b) rLT as functions...Figure 2.8. Slowness curves for a free surface and an incident transverse vertic...Figure 2.9. Moduli of reflection coefficients a) rTT and b) rTL versus the angle...Figure 2.10. Intensity reflection coefficients RLL and RLT and intensity transmi...Figure 2.11. Slowness curves for a solid–fluid interface and an incident transve...Figure 2.12. Intensity reflection coefficients RTL and RTT and intensity transmi...Figure 2.13. Reflection and transmission at a liquid–solid interface. a) Intensi...Figure 2.14. Plate with parallel faces of thickness h immersed in a fluidFigure 2.15. a) Velocity and b) attenuation of longitudinal waves measured in a ...Figure 2.16. Depending on the medium from which it comes, the amplitude of the i...Figure 2.17. Solid with monoclinic symmetry (binary axis parallel to Ox₂). Polar...Figure 2.18. a) Slowness curves of the reflected and transmitted waves generated...

3 Chapter 3Figure 3.1. Disposition of the axesFigure 3.2. Variation of the Rayleigh wave velocity VR with the ratio of the bul...Figure 3.3. a) Displacement and b) stresses of the Rayleigh wave in the depth of...Figure 3.4. Rayleigh wave: a) Deformation of the material as the wave passes thr...Figure 3.5. Evolution of parameters E, I₁ and I₂ depending on the ratio of the b...Figure 3.6. The stiffness of cube A, which has one of its six faces free, is red...Figure 3.7. Variation, with depth, of the longitudinal (L) and transverse (T) co...Figure 3.8. TV and QTH waves propagating in the (001) plane of a cubic crystalFigure 3.9. Phase matching condition between the Rayleigh wave and the QTH wave ...Figure 3.10. Propagation of Rayleigh waves (R), and pseudo-surface acoustic wave...Figure 3.11. Characteristic curves in the XY plane of crystallographic axes for ...Figure 3.12. Capacitor formed of two electrodes in contact with the piezoelectri...Figure 3.13. Methods for investigating surface acoustic wave properties of a cry...Figure 3.14. Waves at the solid-fluid interface, disposition of the axesFigure 3.15. Displacement of the Scholte wave in the liquid (top) and in the sol...Figure 3.16. Fused silica-fluid interface. a) Attenuation of the leaky Rayleigh ...Figure 3.17. Waves at the interface between two solids, arrangement of the axesFigure 3.18. Variation, on both sides of a steel-duralumin interface, of the two...Figure 3.19. Maps of the Stoneley wave velocity (km/s) as functions of the ratio...Figure 3.20. Bleustein–Gulyaev wave in a zinc oxide crystal. Variation of mechan...

4 Chapter 4Figure 4.1. General structure of a guide. The waves propagate along the x1 axisFigure 4.2. The wave travels in the Ox1 direction by successive reflections on t...Figure 4.3. A guided wave presents nodal planes along the walls and also inside ...Figure 4.4. Dispersion curves of an elementary waveguide. At the angular frequen...Figure 4.5. Wave packet: a) Signal at a given time and b) amplitude density as a...Figure 4.6. Signals carried by the Lamb waves a) S₀ and b) A₀ for different prop...Figure 4.7. Phase velocities (solid lines) and group velocities (dashed line) of...Figure 4.8. The Love wave propagates in a structure composed of a plate of thick...Figure 4.9. Phase velocity (solid lines) and group velocity (dashed lines) for t...Figure 4.10. Love waves: a) tangential displacement u₃ and b) stress σ₂₃ in the ...Figure 4.11. The propagation medium, inhomogeneous along x₂, is divided into N s...Figure 4.12. Arrangement of the axes. The plate thickness is d = 2hFigure 4.13. Lamb wave displacement. a) Symmetric: on either side of the median ...Figure 4.14. The (ω, k) plane is divided into three sectors, depending on the va...Figure 4.15. Dispersion curves of the first Lamb modes in a duralumin plate. Sym...Figure 4.16. a) Phase velocities and b) group velocities of the first Lamb modes...Figure 4.17. Particle displacements for a duralumin plate of thickness d =2 mm, ...Figure 4.18. Lamb wave in an isotropic plate. Mechanical displacement of the fir...Figure 4.19. Dispersion curves of the S₅ and S₈ modes for different values of th...Figure 4.20. Normalized cut-off frequencies fcd/VT (solid lines) and fcd/VL (das...Figure 4.21. Variation with Poisson’s ratio (0 ≤ ν ≤ 0.49) of Lamb waves in a fr...Figure 4.22. Specific behavior for ν = 0 (rigid solid). a) Segments of the line ...Figure 4.23. Lamé modes. a) The guided wave is a transverse wave propagating at ...Figure 4.24. a) Dispersion curves of Lamb modes S₀, S₁, S₂, S_2b and of the first...Figure 4.25. Immersed plate. Disposition of axes and components of the wave vect...Figure 4.26. Duralumin plate immersed in water. a) Phase velocity of the fundame...Figure 4.27. a) Plate immersed in water, map of the intensity reflection coeffic...Figure 4.28. Unidirectional composite material made of carbon fibers embedded in...Figure 4.29. Lamb wave slowness curves for a unidirectional composite plate of t...Figure 4.30. Cylindrical waveguide of radius a and coordinates r, θ, zFigure 4.31. Steel cylinder (ν = 0.27). Dispersion curves for the first longitud...Figure 4.32. First three longitudinal modes propagating in a steel cylinder. Var...Figure 4.33. Dispersion curves for the first flexural modes of a steel wire with...Figure 4.34. Dispersion curves for the first torsional modes. The mode T(0,1) is...Figure 4.35. Steel tube (mean radius: 3.75 mm, thickness: 1.5 mm). Variation of ...

5 Appendix 1Figure A1.1. Cylindrical coordinate system. For a color version of this figure, ...Figure A1.2. Spherical coordinate system. For a color version of this figure, se...

6 Appendix 2Figure A2.1. a) Two-dimensional crystalline lattice: all nodes are equivalent, a...Figure A2.2. Rows. The nodes in a two-dimensional lattice are located at the int...Figure A2.3. Miller indices. The spacing between two neighboring lattice planes ...Figure A2.4. A twofold inverse axis (A₂) is equivalent...Figure A2.5. Stereographic projection. a) Triangles SOp and SPN are similar, so ...Figure A2.6. Association of an n-fold direct axis with n perpendicular binary ax...Figure A2.7. The symmetry elements of a cube are Figure A2.8. The 32-point symmetry classes of crystals

7 Appendix 3Figure A3.1. The waves propagate along the x₁ axis of the waveguide. Quantities ...