Acoustics of Layered Media I: Plane and Quasi-Plane Waves

ISBN-13: 9783540647249 / Angielski / Miękka / 1998 / 240 str.

L. M. Brekhovskikh; O. A. Godin; Leonid M. Brekhovskikh

Opis

This monograph is devoted to the systematic presentation of the theory of sound- wave propagation in layered structures. These structures can be man-made, such as ultrasonic filters, lenses, surface-wave delay lines, or natural media, such as the ocean and the atmosphere, with their marked horizontal stratification. A related problem is the propagation of elastic (seismic) waves in the earth's crust These topics have been treated rather completely in the book by L. M. Brek- hovskikh, Waves in Layered Media, the English version of the second edition of which was published by Academic Press in 1980. Due to progress in experimental and computer technology it has become possible to analyze the influence of factors such as medium motion and density stratification upon the propagation of sound waves. Much attention has been paid to propagation theory in near-stratified media, Le., media with small deviations from strict stratification. Interesting results have also been obtained in the fields of acoustics which had been previously considered to be "completely" developed. For these reasons, and also because of the inflow of researchers from the related fields of physics and mathematics, the circle of persons and research groups engaged in the study of sound propagation has rather expanded. Therefore, the appearance of a new summary review of the field of acoustics of layered media has become highly desirable. Since Waves in Layered Media became quite popular, we have tried to retain its positive features and general structure.

Recenzje

"The two books are characterized by scholasticity in the analytical treatment. The analysis is rigorous and complete. This could be attributed to the 'Russian school' where both authors belong to, offering an excellent framework for the study of problems of Mathematical Physics. ...In general, the books are considered valuable for researchers interested in the mathematical modeling of wave phenomena as they provide the readers with a comprehensive coverage of practically all the analytical aspects of the forward problem of acoustic wave propagation. In addition, throughout the books, they will meet many references to non-standard issues, as the propogation in moving media and energy conservation." Michael Taroudakis, Acustica United with Acta Acus, 2000/86/6

Spis treści

1. Basic Equations for Wave Processes in Fluids and Solids.- 1.1 Sound in Layered Fluids.- 1.1.1 Derivation of Wave Equations.- 1.1.2 Plane Waves and Spherical Waves.- 1.1.3 Boundary Conditions.- 1.2 Harmonic Waves.- 1.2.1 Conditions at Infinity.- 1.2.2 Waves with Harmonical Dependence on Horizontal Coordinates and Time.- 1.2.3 Modified Wave Equations.- 1.3 Elastic Waves in Isotropic Solids.- 1.3.1 General Relations.- 1.3.2 Elastic Waves in Homogeneous Solids.- 1.3.3 Elastic Wave Equations in Layered Solids.- 2. Plane Waves in Discretely Layered Fluids.- 2.1 Inhomogeneous Plane Waves. Energy of Sound Waves.- 2.2 Reflection at the Interface of Two Homogeneous Media.- 2.3 Locally Reacting Surfaces.- 2.4 Reflection from a Plane Layer.- 2.4.1 The Input Impedance of a Layer.- 2.4.2 The Reflection and Transmission Coefficients.- 2.4.3 Another Approach to the Reflection and Transmission Coefficients Calculation.- 2.4.4 Two Special Cases.- 2.4.5 Penetration of a Wave Through a Layer.- 2.5 Reflection and Transmission Coefficients for an Arbitrary Number of Layers.- 2.6 Moving Layers. Impedance of Harmonic Waves in Moving Media.- 2.6.1 Sound Wave Impedance in a Moving Medium.- 2.6.2 Plane Wave Reflection from Discretely Layered Moving Media.- 2.6.3 Reflection at a Single Interface.- 3. Monochromatic Plane-Wave Reflection from Continuously Layered Media.- 3.1 General Relations.- 3.2 Solvable Profiles k(z) from the Confluent Hypergeometric Equation.- 3.3 Solvable Profiles Obtained from the Hypergeometric Equation.- 3.4 Plane-Wave Reflection from an Epstein Layer.- 3.4.1 Expressions for Reflection and Transmission Coefficients.- 3.4.2 Transition Epstein Layer.- 3.4.3 Symmetrical Epstein Layer.- 3.5 Reflection of a Plane Wave from a Half-Space with a Linear Law for the Squared Refraction Index.- 3.5.1 The Airy Functions.- 3.5.2 The Case when dn2/dz is Positive.- 3.5.3 The Case when dn2/dz is Negative.- 3.6 Other Cases with Exact Solutions for Normal Incidence.- 3.6.1 Smooth k(z) Profiles.- 3.6.2 “Compound” Layered Media.- 3.7 Exact Solutions for Media with Continuous Stratification of Sound Velocity, Density, and Flow Velocity.- 3.7.1 Motionless Fluid with Density Stratification.- 3.7.2 Moving Layered Medium.- 4. Plane-Wave Reflection from the Boundaries of Solids.- 4.1 Plane Waves in Elastic Half-Spaces with a Free Boundary.- 4.2 Reflection from Solid-Solid and Solid-Fluid Interfaces.- 4.2.1 Two Elastic Half-Spaces in Contact.- 4.2.2 Sound Wave Reflection from Solid.- 4.2.3 Elastic Wave Reflection from Fluid Half-Space.- 4.3 Reflection from a System of Solid Layers.- 4.3.1 Matrix Propagator.- 4.3.2 Reflection Coefficient of the Sound Wave.- 4.3.3 Scattering Matrix for the Elastic Waves.- 4.3.4 Some Special Cases.- 4.4 Surface and “Leaky” Waves.- 4.4.1 A Simple Example of Surface Waves.- 4.4.2 Rayleigh Wave.- 4.4.3 Stoneley and Other Waves at Fluid-Solid and Solid-Solid Interfaces.- 5. Reflection of Sound Pulses.- 5.1 General Relations. Law of Conservation of Integrated Pulse.- 5.1.1 Integral Representation of Sound Field.- 5.1.2 Conservation of Integrated Pulse.- 5.1.3 Energy Conservation.- 5.2 Change of Pulse Shape upon Total Internal Reflection from a Boundary Between Two Homogeneous Media.- 5.3 Total Reflection of a Pulse in Continuously Layered Media.- 6. Universal Properties of the Plane-Wave Reflection and Transmission Coefficients.- 6.1 Symmetry with Respect to Reversion of the Wave Path.- 6.1.1 Sound Waves in Fluids.- 6.1.2 Elastic Waves in Solids.- 6.2 Analytic Properties.- 6.2.1 Poles of the Reflection and Transmission Coefficients.- 6.2.2 Branch Points.- 6.3 Nonreflecting Layers.- 6.3.1 For Any Fixed Frequency and Angle of Incidence a Reflectionless Layer Exists.- 6.3.2 An Example of a Reflectionless Layer for Arbitrary Angle of Incidence.- 6.3.3 An Example of a Reflectionless Layer for Arbitrary Frequency.- 7. Acoustic Waves in Absorbing Anisotropic Media.- 7.1 Absorption of Sound.- 7.1.1 Waves in Dissipative Fluids.- 7.1.2 Absorption in Solids.- 7.2 Anisotropic Elastic Media. Gulyaev-Bluestein Waves.- 7.2.1 The Christoffel Equation.- 7.2.2 Elastic Waves in Transversally Isotropic Solids. Matrix Exponent.- 7.2.3 Harmonic Waves in Piezocrystals.- 7.3 Elastic Properties of Finely Layered Media.- 7.3.1 Matrix Propagator for Inhomogeneous Solids.- 7.3.2 An Effective Medium.- 7.3.3 The Most Important Special Cases.- 8. Geometrical Acoustics. WKB Approximation.- 8.1 The WKB Approximation and Its Range of Validity.- 8.1.1 Asymptotic Solution of the Wave Equation.- 8.1.2 WKB Approximation’s General Conditions of Use.- 8.1.3 Regions of Applicability in Vicinities of Turning Points and Horizons of Resonance Interaction.- 8.2 Physical Meaning of the Approximate Solutions.- 8.2.1 Medium at Rest.- 8.2.2 Moving Medium.- 8.3 Another Approach to the Ray Acoustics Approximation.- 9. The Sound Field in the Case of Turning Horizons and Resonance Interaction with a Flow.- 9.1 Reference Equation Method.- 9.1.1 High-Frequency Solution of the Wave Equation.- 9.1.2 An Estimation of the Asymptotic Solution Accuracy.- 9.1.3 The Simplest Example.- 9.2 Sound Field in the Vicinity of a Turning Point.- 9.3 Reflection from a “Potential Barrier”.- 9.3.1 Uniform Asymptotics of the Sound Field.- 9.3.2 Relation to the WKB Approximation.- 9.3.3 Reflection and Transmission Coefficients.- 9.4 Amplification of Sound in an Inhomogeneous Flow.- 9.4.1 Reference Problem.- 9.4.2 General Flow. Well-Separated Horizon of Resonance Interaction and Turning Points.- 9.4.3 General Flow. Arbitrary Separated Horizon of Resonance Interaction and Turning Points.- 9.4.4 Discussion of the Results.- 10. Sound Reflection from a Medium with Arbitrarily Varying Parameters.- 10.1 Differential Equations for Reflection Coefficient and Impedance of a Sound Wave.- 10.1.1 Riccati Equation.- 10.1.2 Two Properties of the Reflection Coefficient in Inhomogeneous Media.- 10.1.3 On Separation of the Wave Field into Direct and Inverse Waves.- 10.2 Reflection from a Thin Inhomogeneous Layer.- 10.2.1 Reduction of the Problem to an Integral Equation.- 10.2.2 Iterative Solution of the Integral Equation.- 10.2.3 Physical Consequences.- 10.3 Method of Successive Approximations for Weakly Reflecting Layers.- 10.3.1 Integral Equation for the Reflection Coefficient.- 10.3.2 The Born Approximation.- 10.3.3 Numerical Example.- 10.4 Reflection at Interfaces in Continuously Layered Media.- 10.4.1 General Approach.- 10.4.2 Sound Reflection at a Weak Interface.- 10.4.3 Ray Interpretation.- References.