Elastic Waves in Solids, Volume 1

Daniel Royer is a Visiting Professor at the Institut Langevin (Ondes et Images) in Paris, France. His research focuses on the propagation of guided elastic waves and their generation and detection by optical methods. Tony Valier-Brasier is a lecturer at the Jean Le Rond d’Alembert Institute at Sorbonne University in Paris, France. His research focuses on the propagation of elastic waves in multiple scattering media, as well as on guided waves.

• Preface ixList of Main Symbols xiiiChapter 1 Propagation in an Unbounded Solid 11.1 Reviewing the mechanics of continuous media 21.1.1 Conservation equations 21.1.2 Kinematics of continuous media 91.1.3 Poynting’s theorem: energy balance 101.1.4 Stress–strain relationship: Maxwell relations 121.2 Isotropic solid 141.2.1 Constitutive equations 141.2.2 Equations of propagation, wave decoupling 161.2.3 Traveling, plane, sinusoidal waves 211.2.4 Polarization 251.2.5 Acoustic intensity 261.2.6 Cylindrical and spherical waves 271.3 Anisotropic solid 321.3.1 Symmetry and elasticity tensor 321.3.2 Propagation equation, phase velocity, polarization 411.3.3 Propagation in an orthotropic material 431.3.4 Group velocity and energy velocity 451.3.5 Slowness surface and wave surface 481.4 Piezoelectric solid 541.4.1 Constitutive equations 541.4.2 Reduction in the number of independent piezoelectric constants 591.4.3 Plane waves in a piezoelectric crystal 611.5 Viscoelastic media 701.5.1 Constitutive equation of linear viscoelasticity 711.5.2 Simple rheological models 721.5.3 Velocity and attenuation in a viscoelastic medium 741.5.4 Time–temperature superposition principle 771.5.5 Newtonian fluid 78Chapter 2 Reflection and Transmission at an Interface 812.1 Boundary conditions 822.2 Direction and polarization of reflected and transmitted waves 852.2.1 Graphical construction 862.2.2 Wave decoupling 872.2.3 Critical angle, evanescent wave and total reflection 892.2.4 Conservation of energy 912.3 Isotropic solid: transverse horizontal wave 932.3.1 Reflection and transmission between two solids 932.3.2 Plate between two solids, impedance matching 962.4 Isotropic media: longitudinal and transverse vertical waves 1002.4.1 Reflection on a free surface 1002.4.2 Solid–fluid interface 1052.5 Anisotropic medium: diffraction matrix 1162.5.1 Analytical resolution 1172.5.2 Expression for the stresses 1192.5.3 Sorting the solutions 1202.5.4 Considerations of symmetry 1212.5.5 Reflection and transmission coefficients, interface waves 1242.5.6 Interface between an orthotropic solid and an isotropic solid 127Chapter 3 Surface Waves and Interface Waves 1313.1 Surface waves 1323.1.1 Isotropic solid: Rayleigh wave 1323.1.2 Anisotropic solid 1413.1.3 Piezoelectric crystal 1513.2 Interface waves 1643.2.1 Isotropic solid-perfect fluid interface 1643.2.2 Interface between two isotropic solids 1693.3 Bleustein–Gulyaev wave 173Chapter 4 Guided Elastic Waves 1794.1 Waveguide, group velocity 1804.1.1 Elementary planar waveguide 1814.1.2 Velocity of a wave packet 1844.1.3 Propagation of a Gaussian pulse 1874.2 Transverse horizontal waves 1894.2.1 Guided TH modes 1904.2.2 Love wave 1904.2.3 Love wave in an inhomogeneous medium 1924.3 Lamb waves 1964.3.1 Free isotropic plate 1964.3.2 Isotropic plate immersed in a fluid 2214.3.3 Free anisotropic plate 2264.4 Cylindrical guides 2354.4.1 Compressional modes 2394.4.2 Flexural modes 2434.4.3 Torsional modes 2444.4.4 Tubular waveguide 246Appendix 1 Differential Operators in Cylindrical and Spherical Coordinates 247Appendix 2 Symmetry and Tensors 253Appendix 3 Transport of Energy 279References 287Index 295