Computational acoustics : theory and implementation / David R. Bergman.

Format:

Book

Author/Creator:

Bergman, David R., author.

Series:

Wiley series in acoustics, noise and vibration.

THEi Wiley ebooks.

Wiley Series in Acoustics Noise and Vibration

THEi Wiley ebooks

Language:

English

Subjects (All):

Sound-waves--Measurement.

Sound-waves.

Sound-waves--Mathematical models.

Sound-waves--Computer simulation.

Physical Description:

1 online resource (292 pages) : illustrations, tables.

Edition:

1st ed.

Place of Publication:

Hoboken, New Jersey : Wiley, 2018.

System Details:

Access using campus network via VPN at home (THEi Users Only).

Summary:

Covers the theory and practice of innovative new approaches to modelling acoustic propagation There are as many types of acoustic phenomena as there are media, from longitudinal pressure waves in a fluid to S and P waves in seismology. This text focuses on the application of computational methods to the fields of linear acoustics. Techniques for solving the linear wave equation in homogeneous medium are explored in depth, as are techniques for modelling wave propagation in inhomogeneous and anisotropic fluid medium from a source and scattering from objects. Written for both students and working engineers, this book features a unique pedagogical approach to acquainting readers with innovative numerical methods for developing computational procedures for solving problems in acoustics and for understanding linear acoustic propagation and scattering. Chapters follow a consistent format, beginning with a presentation of modelling paradigms, followed by descriptions of numerical methods appropriate to each paradigm. Along the way important implementation issues are discussed and examples are provided, as are exercises and references to suggested readings. Classic methods and approaches are explored throughout, along with comments on modern advances and novel modeling approaches. * Bridges the gap between theory and implementation, and features examples illustrating the use of the methods described * Provides complete derivations and explanations of recent research trends in order to provide readers with a deep understanding of novel techniques and methods * Features a systematic presentation appropriate for advanced students as well as working professionals * References, suggested reading and fully worked problems are provided throughout An indispensable learning tool/reference that readers will find useful throughout their academic and professional careers, this book is both a supplemental text for graduate students in physics and engineering interested in acoustics and a valuable working resource for engineers in an array of industries, including defense, medicine, architecture, civil engineering, aerospace, biotech, and more.

Contents:

Intro

Title Page

Copyright Page

Contents

Series Preface

Chapter 1 Introduction

Chapter 2 Computation and Related Topics

2.1 Floating-Point Numbers

2.1.1 Representations of Numbers

2.1.2 Floating-Point Numbers

2.2 Computational Cost

2.3 Fidelity

2.4 Code Development

2.5 List of Open-Source Tools

2.6 Exercises

References

Chapter 3 Derivation of the Wave Equation

3.1 Introduction

3.2 General Properties of Waves

3.3 One-Dimensional Waves on a String

3.4 Waves in Elastic Solids

3.5 Waves in Ideal Fluids

3.5.1 Setting Up the Derivation

3.5.2 A Simple Example

3.5.3 Linearized Equations

3.5.4 A Second-Order Equation from Differentiation

3.5.5 A Second-Order Equation from a Velocity Potential

3.5.6 Second-Order Equation without Perturbations

3.5.7 Special Form of the Operator

3.5.8 Discussion Regarding Fluid Acoustics

3.6 Thin Rods and Plates

3.7 Phonons

3.8 Tensors Lite

3.9 Exercises

Chapter 4 Methods for Solving the Wave Equation

4.1 Introduction

4.2 Method of Characteristics

4.3 Separation of Variables

4.4 Homogeneous Solution in Separable Coordinates

4.4.1 Cartesian Coordinates

4.4.2 Cylindrical Coordinates

4.4.3 Spherical Coordinates

4.5 Boundary Conditions

4.6 Representing Functions with the Homogeneous Solutions

4.7 Green´s Function

4.7.1 Green´s Function in Free Space

4.7.2 Mode Expansion of Green´s Functions

4.8 Method of Images

4.9 Comparison of Modes to Images

4.10 Exercises

Chapter 5 Wave Propagation

5.1 Introduction

5.2 Fourier Decomposition and Synthesis

5.3 Dispersion

5.4 Transmission and Reflection

5.5 Attenuation

5.6 Exercises

Chapter 6 Normal Modes

6.1 Introduction

6.2 Mode Theory

6.3 Profile Models.

6.4 Analytic Examples

6.4.1 Example 1: Harmonic Oscillator

6.4.2 Example 2: Linear

6.5 Perturbation Theory

6.6 Multidimensional Problems and Degeneracy

6.7 Numerical Approach to Modes

6.7.1 Derivation of the Relaxation Equation

6.7.2 Boundary Conditions in the Relaxation Method

6.7.3 Initializing the Relaxation

6.7.4 Stopping the Relaxation

6.8 Coupled Modes and the Pekeris Waveguide

6.8.1 Pekeris Waveguide

6.8.2 Coupled Modes

6.9 Exercises

Chapter 7 Ray Theory

7.1 Introduction

7.2 High Frequency Expansion of the Wave Equation

7.2.1 Eikonal Equation and Ray Paths

7.2.2 Paraxial Rays

7.3 Amplitude

7.4 Ray Path Integrals

7.5 Building a Field from Rays

7.6 Numerical Approach to Ray Tracing

7.7 Complete Paraxial Ray Trace

7.8 Implementation Notes

7.9 Gaussian Beam Tracing

7.10 Exercises

Chapter 8 Finite Difference and Finite Difference Time Domain

8.1 Introduction

8.2 Finite Difference

8.3 Time Domain

8.4 FDTD Representation of the Linear Wave Equation

8.5 Exercises

Chapter 9 Parabolic Equation

9.1 Introduction

9.2 The Paraxial Approximation

9.3 Operator Factoring

9.4 Pauli Spin Matrices

9.5 Reduction of Order

9.5.1 The Padé Approximation

9.5.2 Phase Space Representation

9.5.3 Diagonalizing the Hamiltonian

9.6 Numerical Approach

9.7 Exercises

Chapter 10 Finite Element Method

10.1 Introduction

10.2 The Finite Element Technique

10.3 Discretization of the Domain

10.3.1 One-Dimensional Domains

10.3.2 Two-Dimensional Domains

10.3.3 Three-Dimensional Domains

10.3.4 Using Gmsh

10.4 Defining Basis Elements

10.4.1 One-Dimensional Basis Elements

10.4.2 Two-Dimensional Basis Elements

10.4.3 Three-Dimensional Basis Elements.

10.5 Expressing the Helmholtz Equation in the FEM Basis

10.6 Numerical Integration over Triangular and Tetrahedral Domains

10.6.1 Gaussian Quadrature

10.6.2 Integration over Triangular Domains

10.6.3 Integration over Tetrahedral Domains

10.7 Implementation Notes

10.8 Exercises

Chapter 11 Boundary Element Method

11.1 Introduction

11.2 The Boundary Integral Equations

11.3 Discretization of the BIE

11.4 Basis Elements and Test Functions

11.5 Coupling Integrals

11.5.1 Derivation of Coupling Terms

11.5.2 Singularity Extraction

11.5.3 Evaluation of the Singular Part

11.5.3.1 Closed-Form Expression for the Singular Part of K

11.5.3.2 Method for Partial Analytic Evaluation

11.5.3.3 The Hypersingular Integral

11.6 Scattering from Closed Surfaces

11.7 Implementation Notes

11.8 Comments on Additional Techniques

11.8.1 Higher-Order Methods

11.8.2 Body of Revolution

11.9 Exercises

Index

EULA.

Notes:

Includes bibliographical references at the end of each chapters and index.

Description based on print version record.

ISBN:

9781119277279

1119277272

9781119277330

1119277337

9781119277323

1119277329

OCLC:

1004981800