Unidirectional Wave Motions
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Unidirectional Wave Motions provides a comprehensive discussion of the formulations and their consequent elaborations which have found demonstrable value in wave analysis. The deliberate focus on unidirectional waves permits a relatively simple mathematical development, without leaving significant gaps in methodology and capability. The book is organized into three parts. The first part deals with the particulars of individual wave equations; the geometry or kinematics of wave forms; and general matters bearing on the transport of energy and momentum as well as dispersion or frequency sensitivity. The second part focuses on aspects of wave generation by localized and extended sources. The third part examines the effects of interaction between specified primary waves and medium irregularities (e.g., obstacles, inclusions, or local variations in the material parameters). Information about these irregularities or scatterers, ranging from microscopic to terrestrial scales, may be gleaned through the attendant phenomena of reflection, refraction, and diffraction, which are fundamental to wave theory.
Table of Contents
Preface
Introduction
Part I
1. Flexible string movements
2. Discontinuous solutions of the wave equation
3. String profiles with a moving vertex
4. Periodic wave functions
5. Variable wave patterns
6. Causality and the superposition of exponential wave functions
7. Conditions for permanence and exponential decay of progressive wave profiles
8. Movements of a heavy chain and a compressible medium
9. A third order (viscoelastic) equation of motion
10. Influence of viscoelasticity on signal transmission
11. String vibrations and the Doppler effect
12. Excitation of a string by a fixed or moving local force
13. Boundary conditions and normal modes of vibration
14. Solution of an inhomogeneous wave equation on a finite coordinate interval
15. Inhomogeneous boundary conditions
16. Wave motions on a string with a point load
17. A Green’s function approach
18. Excitation of a string by the impulsive stimulus of an attached load
19. Characteristic functions and complex eigenfrequencies
20. Resonant reflection and forced motion
Problems 1(a)
21. General excitation of string and oscillator
22. A string with two attached oscillators; matched inner and outer expansions
23. Instantaneous and moving point source functions
24. A densely loaded string
25. A composite or sectionally uniform string
26. Another composite string
27. A multi-section string
28. Initial and boundary value problems for a sectionally uniform string of finite length
29. Excitation of a string with variable length
Problems 1(b)
Part II
30. Interference
31. Energy density and flux
32. Energy propagation and the group velocity
33. Wave kinematics and dispersion
34. Stationary phase
35. An illustrative example
36. Extended initial profiles or ranges of support
37. An envelope of rays or caustic curve
38. Transformation and estimation of contour integrals near saddle points
39. Signal propagation and dispersion
40. Transient solutions of a dispersive wave equation and their ray representation
Problems 11(a)
41. Nonlinear equations for string motions; linearization and other aspects
42. Conservation relations and the pressure exerted by waves
43. Plane electromagnetic waves
44. Mechanical/electrical analogies and impedance concepts for wave propagation
45. Wave propagation along fluid boundaries
46. Source excited gravity waves on a fluid
47. Wave propagation in tubes having elastic walls
Problems 11(b)
48. Scattering matrices
49. A periodically loaded string
50. A periodic coefficient differential equation
51. Green’s functions and the periodically loaded string
52. Selective reflection
53. Average energy flux along the periodically loaded string
54. Forced and free motions of a regularly loaded string
55. Wave motions in a linear chain
56. Green’s functions for the linear chain and applications
57. Causality and dispersion relations
Problems 11(c)
Part III
58. A string with continuously variable density
59. An inhomogeneous segment
60. An inhomogeneous layer
61. Variable wave numbers with a periodic nature
62. Reflection from a periodically composed semi-infinite range
63. Variable wave number profiles with a discontinuous derivative or a null point
64. A multi-parameter family of smooth wave number profiles
65. Connection formulas and their applications
66. Approximate solutions of a wave-like nature for inhomogeneous settings
67. Improvements on the WKBJ or geometrical optics wave functions
68. Integral equation formulations and their consequences
69. Aspects of reflection for inhomogeneous settings
70. Phase calculations and turning points
71. Related equations and improved asymptotic solutions
72. Perturbation calculations in cases of non-uniformity
73. A short wave length expansion technique
74. Variational and other efficient characterizations of scattering coefficients
75. A scattering matrix and its variational characterization
76. Formalities of a variational calculation
77. A Green’s function representation and its variational characterization
78. Other inhomogeneous realizations
79. The Born approximation and reflection at short wave lengths
80. A long wave approximation
81. The Schrödinger wave equation and potential barrier problems
82. Inverse scattering theory
83. Variational theory and its implications
84. Progressive waves in variable configurations
85. A wave speed determination
86. Waves in a random setting
87. The dispersion relation and its role in stability/gain analysis
Problems III
Problems IV
References
Index
Product details
- No. of pages: 514
- Language: English
- Copyright: © North Holland 1978
- Published: January 1, 1978
- Imprint: North Holland
- eBook ISBN: 9780444601957