Nonlinear Wave Processes in Acoustics (Cambridge Texts in Applied Mathematics)

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Nonlinear Wave Processes in Acoustics (Cambridge Texts in Applied Mathematics)

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  • 製本 Hardcover:ハードカバー版/ページ数 298 p.
  • 言語 ENG
  • 商品コード 9780521390804
  • DDC分類 534

Full Description


The investigation of nonlinear phenomena in acoustics has a rich history stretching back to the mechanical physical sciences in the nineteenth century. The study of nonlinear phenomena, such as explosions and jet engines, prompted the sharp growth of interest in nonlinear acoustic phenomena. The authors consider models of different 'acoustic' media as well as equations and behaviour of finite-amplitude waves. Consideration is given to the effects of nonlinearity, dissipation, dispersion, and for two- and three-dimensional problems, reflection and diffraction upon the evolution and interaction of acoustic beams. This book will be of interest not only to specialists in acoustics, but also to a wide audience of mathematicians, physicists, and engineers working on nonlinear waves in various physical systems.

Table of Contents

Preface                                            page vi
1 Nonlinearity, dissipation and dispersion 1 (36)
in acoustics
1.1 Homogeneous gases and liquids 1 (10)
1.2 Isotropic solids 11 (5)
1.3 Liquid with gas bubbles 16 (9)
1.4 Elastic medium with cavities 25 (5)
1.5 "Anomalous" nonlinearities in elastic 30 (7)
media
2 Simple waves and shocks in acoustics 37 (61)
2.1 Nonlinear effects in the presence of 37 (2)
dissipation and dispersion
2.2 Simple waves and discontinuities 39 (10)
2.3 Propagation of pulses 49 (5)
2.4 A medium with finite dissipation 54 (7)
2.5 Propagation of intense acoustic noise 61 (11)
2.6 Waves in media with "anomalous" 72 (6)
nonlinearity
2.7 Sound excitation and amplification by 78 (7)
moving sources
2.8 Finite-amplitude standing waves 85 (5)
2.9 Energy and momentum in a plane sound 90 (8)
wave
3 Nonlinear geometrical acoustics 98 (42)
3.1 Rays and ray tubes 98 (5)
3.2 Nonlinear wave evolution along the rays 103(2)
3.3 Spherical waves 105(7)
3.4 Nonlinear acoustics of explosive waves 112(3)
3.5 One-dimensional propagation in 115(5)
inhomogeneous media
3.6 Refraction of nonlinear waves in a 120(7)
stratified medium
3.7 Self-refraction of shock waves 127(13)
4 Nonlinear sound beams 140(25)
4.1 Paraxial beams 140(2)
4.2 The nonlinear beam equation 142(6)
4.3 Step-by-step technique 148(2)
4.4 Divergent waves 150(8)
4.5 Foci and caustics 158(7)
5 Sound-sound interaction (nondispersive 165(33)
medium)
5.1 One-dimensional interactions 165(11)
5.2 Parametric acoustic transmitters 176(12)
5.3 Parametric sound reception 188(10)
6 Nonlinear acoustic waves in dispersive 198(47)
media
6.1 Media with selective absorption 198(6)
6.2 Nonlinear waves in a waveguide 204(4)
6.3 Parametric amplification and 208(9)
generation of sound
6.4 Acoustic solitons in a liquid with gas 217(3)
bubbles
6.5 Acoustic solitons in solids 220(8)
6.6 Wave interaction in a liquid with 228(7)
resonance bubbles
6.7 Parametric sound transmitter in a 235(10)
waveguide
7 Self-action and stimulated scattering of 245(50)
sound
7.1 Cubic nonlinearity in acoustics 245(5)
7.2 Self-focusing of sound 250(5)
7.3 One-dimensional modulated waves 255(6)
7.4 Stimulated scattering of sound 261(4)
7.5 Wave front reversal 265(8)
7.6 Concentration nonlinearity in a liquid 273(10)
with gas bubbles
7.7 Cavitational self-focusing of sound 283(3)
7.8 Phase locking of nonlinear oscillators 286(9)
in acoustics
Conclusion 295(2)
Subject index 297