PART 1. HOMOGENOUS AND HOMOGENOUS STRATIFIED MEDIA: LINEAR MODEL OF PROPAGATION

Transcription

1 Table of Contents Foreword.... xvii Preface... xxi PART 1. HOMOGENOUS AND HOMOGENOUS STRATIFIED MEDIA: LINEAR MODEL OF PROPAGATION... 1 Chapter 1. Equations of Propagation... 3 Jean-François DE BELLEVAL, Catherine POTEL and Philippe GATIGNOL 1.1. Introduction Fluid medium Elastic solid Solutions of the propagative equation: monochromatic waves, plane waves Fluid medium or isotropic solid Anisotropic solid Bibliography Chapter 2. Interaction of a Plane Wave and a Plane Interface Philippe GATIGNOL, Catherine POTEL and Jean François DE BELLEVAL 2.1. Introduction Boundary conditions in acoustics Plane interface separating two fluid or isotropic solid media Interface separating two anisotropic solid media Bibliography... 59

2 vi Materials and Acoustics Handbook Chapter 3. Propagation of Plane Waves in Multilayered Media Catherine POTEL, Jean François DE BELLEVAL, Michel CASTAINGS and Philippe GATIGNOL 3.1. Introduction Propagation on a single material layer Propagation in a multilayered medium Propagation in a periodic multilayered medium Bibliography Chapter 4. Propagation in Continuously Stratified Media Cécile BARON, Olivier PONCELET, Alexander SHUVALOV and Marc DESCHAMPS 4.1. Introduction Wave equation for 1D inhomogenous media Second-order differential system First-order ordinary differential system for the case of 1D inhomogenity Solution to the wave equation in 1D inhomogenous media The matricant Evaluation of the matricant by the Peano series Remarks on the numerical implementation The Peano series as a power series in dispersion parameters Examples Bibliography Chapter 5. Modal Waves in Plane Structures Philippe GATIGNOL, Catherine POTEL and Jean François DE BELLEVAL 5.1. Introduction General properties of modal waves in plane structures Usual modal waves Dispersion effects for modal waves Generalized modal waves pseudo modal waves A generic example Appendix: non-null elements of determinant D Bibliography PART 2. POROUS AND STRATIFIED POROUS MEDIA LINEAR MODELS OF PROPAGATION Introduction to Part Denis LAFARGE

3 Table of Contents vii Chapter 6. The Equivalent Fluid Model Denis LAFARGE 6.1. Introduction Geometry definitions Ideal fluid Thermoviscous fluids Bibliography Chapter 7. Biot s Model Denis LAFARGE 7.1. Introduction Perfect fluid and elastic solid Thermoviscous fluid and visco-elastic structure Bibliography Chapter 8. Propagation Equations in the Time Domain Zine EL ABIDINE FELLAH, Mohamed FELLAH and Claude DEPOLLIER 8.1. Introduction Materials: frequency and temporal approach Fractional derivative and behavior of materials Fractional derivative and viscoelasticity Fractional derivative and model of the equivalent fluid Inertial regime (high frequency approximation) A semi-infinite medium Cases of a finite medium Reflection and transmission operators Viscous regime (low frequency approximation) Resolution for the semi-infinite medium Solution in a finite medium Reflection and transmission operators Application to Biot s theory Wave propagation in porous materials with a flexible structure Displacement equations Stress-strain relationships Dissipation Mass coefficients ρ ij Equations in the time domain Materials saturated by a liquid Bibliography

4 viii Materials and Acoustics Handbook Chapter 9. Scattering in Porous Media Denis LAFARGE 9.1. Introduction Analysis of multiple scattering in the context of the Independent Scattering Approximation (ISA) Array of cylinders in air Bibliography Chapter 10. Stratified Porous Media Bruno BROUARD Introduction Matrix representation of the propagation in fluid or solid layers Propagation in fluids Propagation in viscoelastic solids reciprocity and antireciprocity Acoustic behavior of a viscoelastic plate Matrix representation of the propagation in porous layers Propagation in porous media with a rigid structure equivalent fluid model Matrix representation of the propagation in porous media with an elastic structure Biot s model Modelization and properties of multilayered media Generalities The matrix representation Evaluation of the properties of multilayered structures Appendices Appendix A: elements of the transfer matrix [T s ] of a viscoelastic solid Appendix B: elements of the impedance matrix [Z s ] of a viscoelastic solid Appendix C: elements of the transfer matrix [T B ] of a porous material with elastic frame Biot s model Appendix D: calculation of the surface impedances on both sides of a multi-layered medium surrounded by two semi-infinite layers of air Appendix E: calculation of the transmission coefficient T n through a multi-layered medium surrounded by two semi-infinite air layers Bibliography

5 Table of Contents ix Chapter 11. Surface Wave Propagation Jean-François ALLARD and Michel HENRY Introduction Summary Porous material heavy-fluid interfaces Porous material light-fluid interfaces Bibliography Chapter 12. The Finite Element Method for Porous Materials Olivier DAZEL and Nicolas DAUCHEZ Introduction Position of the problem Outline of the finite element method History of the finite element method for porous materials Continuous problems considered Boundary problem equations The {u,u} formulation The {u, P} formulation The boundary conditions Poroelastic variational formulations The displacement formulations Mixed formulations Discretized systems Discussion about discretization Conclusion Bibliography PART 3. EXPERIMENTAL AND NUMERICAL METHODS Chapter 13. Transducer for Bulk Waves Daniel ROYER Introduction Piezoelectric materials structures One-dimensional model equivalent circuits Frequency and time responses emitted power Bibliography Chapter 14. Modeling of Ultrasonic Beams Jean-François DE BELLEVAL, Nicolas GENGEMBRE, Alain LHÉMERY and Pierre CALMON Introduction Plane wave decomposition

6 x Materials and Acoustics Handbook Monochromatic regime Impulse regime Decomposition into impulse plane waves The pencil method General principle of modeling an ultrasonic beam using the pencil method The Fermat path Definition of a pencil Propagation of a pencil Reconstruction of the ultrasonic field Example Conclusions Bibliography Chapter 15. Time-Reversal of Waves Mickaël TANTER and Mathias FINK Overview Introduction Time-reversal of acoustic waves: principle Time-reversal cavities and mirrors Time-reversal or temporal and spatial adapted filtering The iterative time-reversal Bibliography Chapter 16. Introduction to Inverse Scattering in Acoustics and Elasticity Marc LAMBERT, Marc BONNET and Dominique LESSELIER General framework Inverse problem of wave scattering Direct problem Optimizations Other approaches General configuration Illustrations Controlled evolution of level sets Topological derivative Bibliography

7 Table of Contents xi PART 4. NONLINEAR ACOUSTICS Chapter 17. Nonlinear Acoustic Phenomena in Micro-inhomogenous Media Vitalyi GUSEV, Vincent TOURNAT and Bernard CASTAGNÈDE Introduction Models of acoustic nonlinearity in micro-inhomogenous media Elastic nonlinearity of an ideal solid Hysteretic nonlinearity of micro-inhomogenous media Nonlinear acoustic waves in micro-inhomogenous materials with hysterisis independent of the strain rate Nonlinear and non-hysteretic absorption in micro-inhomogenous materials Hysteretic nonlinearity of relaxation processes or relaxation of the hysteretic nonlinearity Hertzian nonlinearity in unconsolidated granular materials Conclusions Bibliography Chapter 18. Non-destructive Evaluation of Micro-inhomogenous Solids by Nonlinear Acoustic Methods Vincent TOURNAT, Vitalyi GUSEV and Bernard CASTAGNÈDE Introduction Classic methods Acousto-elasticity Frequency-mixing Nonlinear resonance Modern experiments The Luxembourg-Gorky effect (modulation transfer) Self-modulation instability and bistability Nonlinear acoustic effects with a threshold Conclusions Bibliography PART 5. THE GREEN FUNCTION IN ANISOTROPIC MEDIA Chapter 19. The Cagniard de Hoop Method Olivier PONCELET and Marc DESCHAMPS Introduction Preliminaries Principle of the Cagniard de Hoop method Inhomogenous plane waves Propagation in anisotropic media

8 xii Materials and Acoustics Handbook Equations of elastodynamics Solutions of the homogenous and non-homogenous wave-equation Two-dimensional Green function in an infinite isotropic medium Analysis of the result Why generalized-rays? Graphical interpretation of the Cagniard de Hoop method Some examples of waveforms Two-dimensional Green function in an infinite anisotropic medium Equations of the contours (Cagniard de Hoop polynomial) Practical aspects when using the Cagniard de Hoop contours Examples of waveforms Two-dimensional Lamb problem Isotropic medium Anisotropic medium Three-dimensional Green function on the surface of an anisotropic medium Bibliography PART 6. LINEAR METHODS OF ULTRASONIC NON-DESTRUCTIVE TESTING AND EVALUATION Chapter 20. Measurement of Viscoelastic Modules Michel CASTAINGS Introduction General principle General scheme of an inverse problem Material characterization by measurement of the transmitted ultrasonic field Conclusion Bibliography Chapter 21. Interaction of an Ultrasonic Field with a Composite Plate Philippe GATIGNOL, Catherine POTEL and Jean-François DE BELLEVAL Introduction Geometry of the problem and writing of the fields by spatial Fourier representations Implementation of a field-calculation method by FFT algorithm Bibliography

9 Table of Contents xiii Chapter 22. Flaw Detection by Lamb Waves Catherine POTEL, Philippe GATIGNOL and Jean-François DE BELLEVAL Introduction Transmission control Scan control Control using the stress distribution Deviation of the Lamb wave beam Bibliography Chapter 23. Non-Destructive Testing of Concrete by Ultrasonic Methods. 609 Vincent GARNIER, Jean-François CHAIX and Gilles CORNELOUP Non-destructive testing of concrete by ultrasonic methods The material Implementation of ultrasonic measurements Examples of applications and developments Homogenization applied to concrete Conclusions Bibliography Chapter 24. Non-Destructive Evaluation and Testing and Structural Health Monitoring of Composite Materials by Ultrasound and Acoustic Emission Rachid El GUERJOUMA, Anne MAREC, Hanane NECHAD and Jean-Hugh THOMAS Introduction Health monitoring of polymer matrix based composites in hygrothermal ageing On-site health monitoring of polymer based composites stressed in creep: global ultrasonic and acoustic emission approach Conclusions Bibliography PART 7. CHARACTERIZATION OF POROELASTIC MATERIALS Chapter 25. Metrology of Physical Parameters of Absorbing Materials Michel HENRY, Christophe AYRAULT, Bernard CASTAGNÈDE, Zine EL ABIDINE FELLAH, Claude DEPOLLIER, Mohamed FELLAH, Walter LAURIKS and Sohbi SAHRAOUI Introduction Acoustical parameters Mechanical parameters Bibliography

10 xiv Materials and Acoustics Handbook Chapter 26. Metrology of Acoustical Properties of Absorbing Materials: Surface Impedance Michel HENRY Introduction Method of the Kundt tube T.M.T.C. method of the Kundt tube Other methods: Chung and Blaser Bibliography Chapter 27. The Nearfield Acoustical Holography Method Bruno BROUARD Principles of the acoustical holography Application to plane geometries Backpropagation Physical interpretation Principle of the experience developed by Tamura Hypothesis Theory Some remarks Appendix A: 2D Fourier transform in cylindrical coordinates Bibliography Chapter 28. Prediction of Acoustic Properties of Multilayer Structures Some Examples of Applications Nicolas DAUCHEZ Introduction Absorption Insulation Bibliography PART 8. BIOMEDICAL FIELD Chapter 29. Ultrasonic Characterization of the Bone Marie-Christine HO BA THO and Pascal LAUGIER Introduction In-vitro determination of acoustical and elastic properties In vivo determination of acoustic properties (ultrasonic bone mineral density test) Simulation and inverse problems Bibliography

11 Table of Contents xv Chapter 30. Medical Ultrasonography François TRANQUART, Aurore BLEUZEN, Bruno RICHARD and Léandre POURCELOT Introduction Principles, technology, acquisitions and parameters of influence Ultrasound modes Vascular study by ultrasonic Doppler Nonlinear ultrasound imaging Medical applications of ultrasound Bibliography Chapter 31. Use of Time-reversal Mickaël TANTER and Mathias FINK Use of time-reversal Monitoring and destruction of kidney stones by time-reversal Ultrasound focalization in the brain by time-reversal Time-reversal mirror for brain therapy by ultrasound Bibliography Chapter 32. Elastography Stefan CATHELINE and Rémi SOUCHON Introduction Quasi-static elastography Dynamic and transient elastography Bibliography Chapter 33. Ultrasound and Therapy Cyril LAFON, Dominique CATHIGNOL and Jean-Yves CHAPELON Introduction Shock waves and extracorporeal lithotripsy High intensity focused ultrasounds for ultrasound surgery Conclusion Bibliography Chapter 34. Ultrasound Characterization of Bone Tissues by Poroelastic Theories Naima SEBAA, Zine EL ABIDINE FELLAH, Claude DEPOLLIER and Walter LAURIKS Introduction Model Longitudinal wave Transmission and reflection operators

12 xvi Materials and Acoustics Handbook Inverse problem Experimental set-up and results Conclusion Bibliography Chapter 35. Acoustic Tomography, Ultrasonic Tomography Jean-Pierre LEFEBVRE, Philippe LASAYGUES, and Serge MENSAH Introduction Tomography and inverse propagation/scattering Ultrasonic transmission tomography Ultrasonic diffraction tomography Conclusion Bibliography List of Authors Index