Unidirectional Wave Motions

Unidirectional Wave Motions

1st Edition - January 1, 1978

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  • Author: H. Levine
  • eBook ISBN: 9780444601957

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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


    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



Product details

  • No. of pages: 514
  • Language: English
  • Copyright: © North Holland 1978
  • Published: January 1, 1978
  • Imprint: North Holland
  • eBook ISBN: 9780444601957

About the Author

H. Levine

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