Elastic Waves in Solids, Volume 1 : Propagation

Elastic waves are used in fields as diverse as the non-destructive evaluation of materials, medicine, seismology and telecommunications. Elastic Waves in Solids 1 presents the different modes of propagation of elastic waves in increasingly complex media and structures. It first studies the propagation in an unlimited solid where only the material properties are taken into account. It then analyzes reflection and transmission phenomena at an interface with a fluid or a second solid. It explains the search for propagation modes on a free surface or at the interface between two media. Finally, it proposes a study of the dispersive propagation of elastic waves guided by a plate or a cylinder. This book is intended for students completing a master’s degree in acoustics, mechanics, geophysics or engineering, as well as teachers and researchers in these disciplines. Cover Half-Title Page Title Page Copyright Page Contents Preface List of Main Symbols 1. Propagation in an Unbounded Solid 1.1. Reviewing the mechanics of continuous media 1.1.1. Conservation equations 1.1.2. Kinematics of continuous media 1.1.3. Poynting’s theorem: energy balance 1.1.4. Stress–strain relationship: Maxwell relations 1.2. Isotropic solid 1.2.1. Constitutive equations 1.2.2. Equations of propagation, wave decoupling 1.2.3. Traveling, plane, sinusoidal waves 1.2.4. Polarization 1.2.5. Acoustic intensity 1.2.6. Cylindrical and spherical waves 1.3. Anisotropic solid 1.3.1. Symmetry and elasticity tensor 1.3.2. Propagation equation, phase velocity, polarization 1.3.3. Propagation in an orthotropic material 1.3.4. Group velocity and energy velocity 1.3.5. Slowness surface and wave surface 1.4. Piezoelectric solid 1.4.1. Constitutive equations 1.4.2. Reduction in the number of independent piezoelectric constants 1.4.3. Plane waves in a piezoelectric crystal 1.5. Viscoelastic media 1.5.1. Constitutive equation of linear viscoelasticity 1.5.2. Simple rheological models 1.5.3. Velocity and attenuation in a viscoelastic medium 1.5.4. Time–temperature superposition principle 1.5.5. Newtonian fluid 2. Reflection and Transmission at an Interface 2.1. Boundary conditions 2.2. Direction and polarization of reflected and transmitted waves 2.2.1. Graphical construction 2.2.2. Wave decoupling 2.2.3. Critical angle, evanescent wave and total reflection 2.2.4. Conservation of energy 2.3. Isotropic solid: transverse horizontal wave 2.3.1. Reflection and transmission between two solids 2.3.2. Plate between two solids, impedance matching 2.4. Isotropic media: longitudinal and transverse vertical waves 2.4.1. Reflection on a free surface 2.4.2. Solid–fluid interface 2.5. Anisotropic medium: diffraction matrix 2.5.1. Analytical resolution 2.5.2. Expression for the stresses 2.5.3. Sorting the solutions 2.5.4. Considerations of symmetry 2.5.5. Reflection and transmission coefficients, interface waves 2.5.6. Interface between an orthotropic solid and an isotropic solid 3. Surface Waves and Interface Waves 3.1. Surface waves 3.1.1. Isotropic solid: Rayleigh wave 3.1.2. Anisotropic solid 3.1.3. Piezoelectric crystal 3.2. Interface waves 3.2.1. Isotropic solid-perfect fluid interface 3.2.2. Interface between two isotropic solids 3.3. Bleustein–Gulyaev wave 4. Guided Elastic Waves 4.1. Waveguide, group velocity 4.1.1. Elementary planar waveguide 4.1.2. Velocity of a wave packet 4.1.3. Propagation of a Gaussian pulse 4.2. Transverse horizontal waves 4.2.1. Guided TH modes 4.2.2. Love wave 4.2.3. Love wave in an inhomogeneous medium 4.3. Lamb waves 4.3.1. Free isotropic plate 4.3.2. Isotropic plate immersed in a fluid 4.3.3. Free anisotropic plate 4.4. Cylindrical guides 4.4.1. Compressional modes 4.4.2. Flexural modes 4.4.3. Torsional modes 4.4.4. Tubular waveguide Appendix 1. Differential Operators in Cylindrical and Spherical Coordinates A1.1. Cylindrical coordinates A1.2. Spherical coordinates Appendix 2. Symmetry and Tensors A2.1. Crystalline structure A2.1.1. Lattice and atomic structure A2.1.2. Rows, lattice planes and cells A2.2. Point symmetry of crystals A2.2.1. Point symmetry operations A2.2.2. Point symmetry of lattices: the seven crystal systems A2.2.3. The 32-point symmetry classes of crystals A2.3. Representation of physical properties of crystals by tensors A2.3.1. Change of orthonormal reference axes A2.3.2. Definition of a tensor A2.4. Reduction of the number of independent components imposed by the symmetry elements A2.4.1. Matrices of point symmetry operations A2.4.2. Effect of a center of symmetry A2.5. Reduction of the number of independent elastic constants A2.5.1. Crystals with at least one binary axis A2.5.2. Crystals with a principal axis An (n > 2) Appendix 3. Transport of Energy A3.1. Energy balance A3.2. Harmonic case A3.3. Susceptance and free modes References Chapter 1 Chapter 2 Chapter 3 Chapter 4 Appendixes General bibliography Index Other titles from iSTE in Waves