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Unidirectional Wave Motions

1st Edition - January 1, 1978

Author: H. Levine

eBook ISBN:

9 7 8 - 0 - 4 4 4 - 6 0 1 9 5 - 7

Unidirectional Wave Motions provides a comprehensive discussion of the formulations and their consequent elaborations which have found demonstrable value in wave analysis. The… Read more

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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.

PrefaceIntroductionPart 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 IVReferencesIndex