Nonlinear Wave Processes in Acoustics

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Cambridge University Press, May 28, 1998 - Mathematics - 298 pages
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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. In this book, the authors consider models of different "acoustic" media as well as equations and behavior of finite-amplitude waves. The authors also consider the effects of nonlinearity, dissipation, dispersion, and for two- and three-dimensional problems, reflection and diffraction on 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.
  

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Contents

Nonlinearity dissipation and dispersion in acoustics
1
12 Isotropic solids
11
13 Liquid with gas bubbles
16
14 Elastic medium with cavities
25
15 Anomalous nonlinearities in elastic media
30
Simple waves and shocks in acoustics
37
22 Simple waves and discontinuities
39
23 Propagation of pulses
49
44 Divergent waves
150
45 Foci and caustics
158
Soundsound interaction nondispersive medium
165
52 Parametric acoustic transmitters
176
53 Parametric sound reception
188
Nonlinear acoustic waves in dispersive media
198
62 Nonlinear waves in a waveguide
204
63 Parametric amplification and generation of sound
208

Burgers equation
54
25 Propagation of intense acoustic noise
61
26 Waves in media with anomalous nonlinearity
72
27 Sound excitation and amplification by moving sources
78
28 Finiteamplitude standing waves
85
29 Energy and momentum in a plane sound wave
90
Nonlinear geometrical acoustics
98
32 Nonlinear wave evolution along the rays
103
33 Spherical waves
105
34 Nonlinear acoustics of explosive waves
112
35 Onedimensional propagation in inhomogeneous media Waves in the atmosphere
115
36 Refraction of nonlinear waves in a stratified medium
120
37 Selfrefraction of shock waves
127
Nonlinear sound beams
140
42 The nonlinear beam equation
142
43 Stepbystep technique
148
64 Acoustic solitons in a liquid with gas bubbles
217
65 Acoustic solitons in solids
220
66 Wave interaction in a liquid with resonance bubbles
228
67 Parametric sound transmitter in a waveguide
235
Selfaction and stimulated scattering of sound
245
72 Selffocusing of sound
250
73 Onedimensional modulated waves
255
74 Stimulated scattering of sound
261
75 Wave front reversal
265
76 Concentration nonlinearity in a liquid with gas bubbles
273
77 Cavitational selffocusing of sound
283
78 Phase locking of nonlinear oscillators in acoustics
286
Conclusion
295
Subject index
297
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