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E-raamat: Computational Acoustics - Theory and Implementation: Theory and Implementation [Wiley Online]

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Computational Acoustics - Theory and Implementation: Theory and ImplementationSuurem pilt
Teised raamatud teemal:
Wiley Online e-raamatudRohkem infot Wiley Online kohta
Raamatu kodulehekülg: https://onlinelibrary.wiley.com/doi/book/10.1002/9781119277323

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.

Series Preface ix
1 Introduction
1(4)
2 Computation and Related Topics
5(14)
2.1 Floating-Point Numbers
5(4)
2.1.1 Representations of Numbers
5(2)
2.1.2 Floating-Point Numbers
7(2)
2.2 Computational Cost
9(2)
2.3 Fidelity
11(1)
2.4 Code Development
12(4)
2.5 List of Open-Source Tools
16(1)
2.6 Exercises 17 References
17(2)
3 Derivation of the Wave Equation
19(30)
3.1 Introduction
19(1)
3.2 General Properties of Waves
20(3)
3.3 One-Dimensional Waves on a String
23(3)
3.4 Waves in Elastic Solids
26(3)
3.5 Waves in Ideal Fluids
29(12)
3.5.1 Setting Up the Derivation
29(1)
3.5.2 A Simple Example
30(1)
3.5.3 Linearized Equations
31(2)
3.5.4 A Second-Order Equation from Differentiation
33(1)
3.5.5 A Second-Order Equation from a Velocity Potential
34(2)
3.5.6 Second-Order Equation without Perturbations
36(1)
3.5.7 Special Form of the Operator
36(4)
3.5.8 Discussion Regarding Fluid Acoustics
40(1)
3.6 Thin Rods and Plates
41(1)
3.7 Phonons
42(1)
3.8 Tensors Lite
42(6)
3.9 Exercises 48 References
48(1)
4 Methods for Solving the Wave Equation
49(36)
4.1 Introduction
49(1)
4.2 Method of Characteristics
49(7)
4.3 Separation of Variables
56(1)
4.4 Homogeneous Solution in Separable Coordinates
57(6)
4.4.1 Cartesian Coordinates
58(1)
4.4.2 Cylindrical Coordinates
59(2)
4.4.3 Spherical Coordinates
61(2)
4.5 Boundary Conditions
63(4)
4.6 Representing Functions with the Homogeneous Solutions
67(3)
4.7 Green's Function
70(6)
4.7.1 Green's Function in Free Space
70(2)
4.7.2 Mode Expansion of Green's Functions
72(4)
4.8 Method of Images
76(5)
4.9 Comparison of Modes to Images
81(1)
4.10 Exercises
82(3)
References
82(3)
5 Wave Propagation
85(14)
5.1 Introduction
85(1)
5.2 Fourier Decomposition and Synthesis
85(3)
5.3 Dispersion
88(2)
5.4 Transmission and Reflection
90(6)
5.5 Attenuation
96(1)
5.6 Exercises
97(2)
References
97(2)
6 Normal Modes
99(38)
6.1 Introduction
99(1)
6.2 Mode Theory
100(1)
6.3 Profile Models
101(4)
6.4 Analytic Examples
105(5)
6.4.1 Example 1: Harmonic Oscillator
105(3)
6.4.2 Example 2: Linear
108(2)
6.5 Perturbation Theory
110(8)
6.6 Multidimensional Problems and Degeneracy
118(2)
6.7 Numerical Approach to Modes
120(9)
6.7.1 Derivation of the Relaxation Equation
120(5)
6.7.2 Boundary Conditions in the Relaxation Method
125(2)
6.7.3 Initializing the Relaxation
127(1)
6.7.4 Stopping the Relaxation
128(1)
6.8 Coupled Modes and the Pekeris Waveguide
129(6)
6.8.1 Pekeris Waveguide
129(2)
6.8.2 Coupled Modes
131(4)
6.9 Exercises
135(2)
References
135(2)
7 Ray Theory
137(40)
7.1 Introduction
137(1)
7.2 High Frequency Expansion of the Wave Equation
138(6)
7.2.1 Eikonal Equation and Ray Paths
139(1)
7.2.2 Paraxial Rays
140(4)
7.3 Amplitude
144(1)
7.4 Ray Path Integrals
145(15)
7.5 Building a Field from Rays
160(2)
7.6 Numerical Approach to Ray Tracing
162(6)
7.7 Complete Paraxial Ray Trace
168(2)
7.8 Implementation Notes
170(1)
7.9 Gaussian Beam Tracing
171(2)
7.10 Exercises
173(4)
References
174(3)
8 Finite Difference and Finite Difference Time Domain
177(22)
8.1 Introduction
177(1)
8.2 Finite Difference
178(10)
8.3 Time Domain
188(5)
8.4 FDTD Representation of the Linear Wave Equation
193(4)
8.5 Exercises
197(2)
References
197(2)
9 Parabolic Equation
199(16)
9.1 Introduction
199(1)
9.2 The Paraxial Approximation
199(2)
9.3 Operator Factoring
201(3)
9.4 Pauli Spin Matrices
204(1)
9.5 Reduction of Order
205(5)
9.5.1 The Pade Approximation
207(1)
9.5.2 Phase Space Representation
208(1)
9.5.3 Diagonalizing the Hamiltonian
209(1)
9.6 Numerical Approach
210(2)
9.7 Exercises
212(3)
References
212(3)
10 Finite Element Method
215(28)
10.1 Introduction
215(1)
10.2 The Finite Element Technique
216(2)
10.3 Discretization of the Domain
218(7)
10.3.1 One-Dimensional Domains
218(1)
10.3.2 Two-Dimensional Domains
219(3)
10.3.3 Three-Dimensional Domains
222(1)
10.3.4 Using Gmsh
223(2)
10.4 Defining Basis Elements
225(7)
10.4.1 One-Dimensional Basis Elements
226(1)
10.4.2 Two-Dimensional Basis Elements
227(2)
10.4.3 Three-Dimensional Basis Elements
229(3)
10.5 Expressing the Helmholtz Equation in the FEM Basis
232(2)
10.6 Numerical Integration over Triangular and Tetrahedral Domains
234(6)
10.6.1 Gaussian Quadrature
234(1)
10.6.2 Integration over Triangular Domains
235(4)
10.6.3 Integration over Tetrahedral Domains
239(1)
10.7 Implementation Notes
240(1)
10.8 Exercises
240(3)
References
241(2)
11 Boundary Element Method
243(30)
11.1 Introduction
243(1)
11.2 The Boundary Integral Equations
244(5)
11.3 Discretization of the BIE
249(4)
11.4 Basis Elements and Test Functions
253(1)
11.5 Coupling Integrals
254(13)
11.5.1 Derivation of Coupling Terms
254(2)
11.5.2 Singularity Extraction
256(4)
11.5.3 Evaluation of the Singular Part
260(1)
11.5.3.1 Closed-Form Expression for the Singular Part of K
260(1)
11.5.3.2 Method for Partial Analytic Evaluation
261(5)
11.5.3.3 The Hypersingular Integral
266(1)
11.6 Scattering from Closed Surfaces
267(2)
11.7 Implementation Notes
269(2)
11.8 Comments on Additional Techniques
271(2)
11.8.1 Higher-Order Methods
271(1)
11.8.2 Body of Revolution
272(1)
11.9 Exercises
273(1)
References 273(2)
Index 275
David R. Bergman, PhD is Owner and Chief Scientist, Exact Solution Scientific Consulting LLC. He has a PhD in physics with a specialization in General Relativity and High Energy Theory. Among other things, he has developed simulations for testing algorithms used in acoustics, modeled electromagnetic remote sensing devices, and modeled underwater and aero-acoustic propagation, acoustic propagation in transducer layers, and performed mechanical vibrational analysis in bio mechanical systems.
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