Acoustic high-frequency diffraction theory / Frédéric Molinet.

Format:

Book

Author/Creator:

Molinet, Frédéric.

Language:

English

Subjects (All):

Sound-waves--Diffraction--Mathematical models.

Physical Description:

1 online resource (512 p.)

Edition:

1st ed.

Place of Publication:

[New York, N.Y.] (222 East 46th Street, New York, NY 10017) : Momentum Press, 2011.

Language Note:

English

Summary:

This book was written for researchers and engineers working with aerial and underwater acoustics. It examines the interactions of acoustic waves with obstacles that may be rigid, soft, elastic, or characterized by an impedance boundary condition. The approach is founded on asymptotic high-frequency diffraction methods based on the concept of rays. Despite the progress in the field of numerical methods for diffraction problems, ray methods remain the most useful approximate methods for analyzing wave motions. Ray methods provide considerable physical insight into diffraction mechanisms and allow for the analytic treatment of objects that are still too large in terms of wavelength to be solved in the realm of numerical methods.

Contents:

List of figures

List of tables

About the author

Preface

1. Introduction to the geometrical theory of diffraction

1.1. General overview and basic concepts

1.2. The Fermat principle

Conditions for a path to be a ray

Application of conditions (1.5) and (1.6) to specific problems

Segments in a fluid with constant sound velocity

Reflection from a smooth surface

Transmission through a smooth interface between two different homogeneous fluids

Excitation of elastic waves at a smooth interface between a homogeneous fluid and an isotropic homogeneous elastic body

Diffraction by an edge in a homogeneous fluid

Surface rays

1.3. Extension of Fermat's principle to surface waves

Planar interface

Curved interface

1.4. Fundamentals of asymptotic expansions

Asymptotic sequence

Compatible asymptotic sequence

Properties of an asymptotic expansion

1.5. Asymptotic solution of the wave equation in a source-free unbounded medium

Derivation of the asymptotic expansion of the solution

Resolution of the Eikonal equation

Properties of the characteristic curves

Resolution of the transport equation

1.6. Acoustic field reflected by a smooth, rigid, soft or impedance surface

1.7. Reflected and transmitted waves at a smooth interface between a fluid and an elastic medium

1.8. Acoustic field diffracted by the edge of an impenetrable wedge

1.9. Acoustic field in the shadow zone of a smooth convex object

References

2. Canonical problems and nonuniform asymptotic theory of acoustic wave diffraction

2.1. Introduction

2.2. The wedge

Hard and soft straight wedge at normal and oblique incidence

Line source excitation

Plane wave incidence

Impedance wedge at normal and oblique incidence: Maliuzhinets's solution

Analytical details for the justification of the general form of the solution

Derivation of the solution

Asymptotic evaluation of the solution

Generalization to oblique incidence

Elastic wedge-shaped shell

Generalization of the elastic wedge-shaped shell solution to oblique incidence

Typical examples

2.3. The circular cylinder

Circular cylinder with hard, soft, or impedance boundary conditions

General solution to the problem

Asymptotic expansion and physical interpretation of the solution

Expression of the diffraction coefficient

Noncircular convex cylinder

Field at an observation point located on the surface of a circular cylinder

Position of the poles in the complex v-plane

Oblique incidence

Three-dimensional convex surface with hard soft, or impedance boundary conditions

Hollow elastic circular cylinder

General solution for normal incidence

Watson transformation

Field diffracted in the shadow region by creeping waves

Noncircular convex cylindrical shell

Oblique incidence for creeping waves

Elastic surface waves

Oblique incidence for elastic surface waves

Noncircular cylindrical shell at normal and oblique incidence

Three-dimensional convex shell

General solution for creeping waves

General solution for elastic surface waves

2.4. Concave surface

Introduction

Solution of the canonical problem of a line source parallel to the generatrix of a concave circular cylinder

Extraction of the GA contributions

Expression of the remainder integral

Extension of the solution to more generalized situations

3. Uniform asymptotic theory of acoustic wave diffraction

3.1. Introduction

3.2. The three-dimensional convex wedge

Uniform solution for the acoustic field scattered by a convex three-dimensional hard or soft wedge

Uniform asymptotic solution of a hard or soft wedge with planar faces submitted to a planar sound wave

Uniform asymptotic solutions for a soft or hard wedge with curved faces

Uniform asymptotic solutions for the acoustic field scattered by a convex impedance wedge

Uniform asymptotic solution of an impedance wedge with planar faces

Uniform asymptotic solution for a general three-dimensional impedance wedge

Uniform asymptotic solutions for the acoustic field scattered by a convex wedge-shaped elastic shell

Uniform asymptotic solution for a wedge-shaped shell with planar faces

Uniform asymptotic solution for a three-dimensional wedge-shaped shell

3.3. The three-dimensional smooth convex surface

Uniform asymptotic solution through the shadow boundary of a smooth convex two-dimensional surface

Uniform asymptotic solution for a circular impedance cylinder

Uniform asymptotic solution for a smooth convex impedance cylinder

Field in the boundary layer of a smooth convex impedance cylinder

Uniform asymptotic solution through the shadow boundary of a smooth convex three-dimensional surface

3.4. The three-dimensional smooth convex shell

Uniform solution for a hollow elastic cylinder

Uniform solution for the GA field associated with the creeping wave field

Uniform solution for the reflected field associated with the elastic surface wave field

Noncircular cylindrical shell

Uniform solution for a three-dimensional convex shell

Uniform solution for creeping waves

Uniform solution for elastic surface waves

3.5. Numerical results

Results concerning the wedge

Results concerning the circular cylinder

4. Wave field near a caustic

4.1. Introduction

4.2. Techniques for calculating the field on a caustic and in its neighborhood

Observation point located close to a regular caustic

Canonical problem for a regular caustic

Uniform asymptotic expansion for a regular three-dimensional caustic

Caustic of rays reflected by a smooth surface

Caustic of rays diffracted by an edge

Caustic of rays diffracted by a smooth surface (creeping rays)

Comments on the solutions for a regular caustic

Observation point located close to a line cusp of a caustic

5. Hybrid diffraction coefficients

5.1. Introduction

5.2. Edge-excited and edge-diffracted creeping waves

Spectral representation of the Fock field on a smooth convex cylindrical surface

Hybrid diffraction coefficients for creeping waves on a curved wedge

Two-dimensional wedge

Three-dimensional wedge

Solution valid at grazing incidence and grazing observation

5.3. Edge-excited and edge-diffracted surface waves

Impedance wedge

Elastic surface wave on a curved wedge

5.4. Edge-excited and edge-diffracted whispering gallery waves

Appendix A. A brief presentation of the governing equations for wave processes in fluids

A.1. Wave propagation in ideal fluids

A.2. Sound waves

A.3. Boundary conditions

Absolutely rigid boundary

Absolutely soft boundary

Interface between two fluids at rest

A.4. Harmonic waves

A.5. Reflection at a boundary

Impedance boundary

A.6. Reflection and refraction at the interface of two homogeneous fluids

Appendix B. A brief presentation of the governing equations of linearized elasticity

B.1. Deformation

B.2 Linear momentum and stress tensor

B.3. Hooke's law

B.4. Waves in an elastic medium

B.5. Boundary conditions at interfaces

B.6. Elastic waves in homogeneous isotropic solids

B.7. Harmonic waves

B.8. Reflection and refraction at a plane interface

B.9. Reflection on an elastic plate separating a fluid from vacuum

Application of the boundary conditions

Solution of the system of linear equations

Appendix C. Surface waves

C.1. Introduction

C.2. Rayleigh waves

C.3. Surface waves at fluid-solid interfaces

C.4. Leaky waves

Appendix D. General formulas for the principal radii of curvature of the reflected wave front on a three-dimensional surface

Appendix E. Symmetric form of the Maliuzhinets diffraction coefficient

Appendix F. Elements of the determinant of the boundary conditions for a circular elastic shell in a fluid

F.1. Normal incidence

F.2. Oblique incidence

Index.

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Title from PDF t.p. (viewed on April 21, 2011).

ISBN:

1-283-89571-4

1-60650-102-X

OCLC:

778886187