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Wave Propagation in Solids and Fluids

The purpose of this volume is to present a clear and systematic account of the mathematical methods of wave phenomena in solids, gases, and water that will be readily accessible to physicists and engineers. The emphasis is on developing the necessary mathematical techniques, and on showing how these...

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Bibliographic Details
Main Author: Davis, Julian L.
Format: eBook
Language:English
Published: New York, NY Springer New York 1988, 1988
Edition:1st ed. 1988
Subjects:
Engineering Fluid Dynamics
Fluid Mechanics
Classical And Continuum Physics
Engineering
Classical Mechanics
Continuum Mechanics
Acoustics
Physics
Technology And Engineering
Mechanics
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 9.14. Hamilton-Jacobi Theory
  • 9.15. Characteristic Theory in Relation to Hamilton-Jacobi Theory
  • 9.16. Principle of Least Action
  • 9.17. Hamilton-Jacobi Theory and Wave Propagation
  • 9.18. Application to Quantum Mechanics.-9.19. Asymptotic Phenomena
  • 3.4. Method of Characteristics for Second-Order Partial Differential Equations
  • 3.5. Propagation of Discontinuities
  • 3.6. Canonical Form for Second-Order Partial Differential Equations with Constant Coefficients
  • 3.7. Conservation Laws, Weak Solutions
  • 3.8. Divergence Theorem, Adjoint Operator, Green’s Identity, Riemann’s Method
  • 4 Transverse Vibrations of Strings
  • 4.1. Solution of the Wave Equation, Characteristic Coordinates
  • 4.2. D’Alembert’s Solution
  • 4.3. Nonhomogeneous Wave Equation
  • 4.4. Mixed Initial Value and Boundary Value Problem, Finite String
  • 4.5. Finite or Lagrange Model for Vibrating String
  • 5 Water Waves
  • 5.1. Conservation Laws
  • 5.2. Potential Flow
  • 5.3. Two-Dimensional Flow, Complex Variables
  • 5.4. The Drag Force Past a Body in Potential Flow
  • 5.5. Energy Flux
  • 5.6. Small Amplitude Gravity Waves
  • 5.7. Boundary Conditions
  • 5.8. Formulation of a Typical Surface Wave Problem
  • 5.9. Simple Harmonic Oscillations in Water at Constant Depth
  • 5.10. The Solitary Wave
  • 5.11. Approximation Theories
  • 6 Sound Waves
  • 6.1. Linearization of the Conservation Laws
  • 6.2. Plane Waves
  • 6.3. Energy and Momentum
  • 6.4. Reflection and Refraction of Sound Waves
  • 6.5. Sound Wave Propagation in a Moving Medium
  • 6.6. Spherical Sound Waves
  • 6.7. Cylindrical Sound Waves
  • 6.8. General Solution of the Wave Equation
  • 6.9. Huyghen’s Principle
  • 7 Fluid Dynamics
  • I. Inviscid Fluids
  • 7.1. One-Dimensional Compressible Inviscid Flow
  • 7.2. Two-Dimensional Steady Flow
  • 7.3. Shock Wave Phenomena
  • II. Viscous Fluids
  • 7.4. Viscosity, Elementary Considerations
  • 7.5. Conservation Laws for a Viscous Fluid
  • 7.6. Flow in a Pipe, Poiseuille Flow
  • 7.7. Dimensional Considerations
  • 7.8. Stokes’s Flow
  • 7.9. Oscillatory Motion
  • 7.10. Potential Flow
  • 8 Wave Propagation in Elastic Media
  • Historical Introduction to Wave Propagation
  • 8.1. Fundamental Concepts of Elasticity
  • 8.2. Equations of Motion for the Stress Components
  • 8.3. Equations of Motion for the Displacement, Navier Equations
  • 8.4. Propagation of a Plane Elastic Wave
  • 8.5. Spherically Symmetric Waves
  • 8.6. Reflection of Plane Waves at a Free Surface
  • 8.7. Surface Waves, Rayleigh Waves
  • 9 Variational Methods in Wave Phenomena
  • 9.1. Principle of Least Time
  • 9.2. One-Dimensional Treatment, Euler’s Equation
  • 9.3. Euler’s Equations for the Two-Dimensional Case
  • 9.4. Generalization to Functional with More Than One Dependent Variable
  • 9.5. Hamilton’s Variational Principle
  • 9.6. Lagrange’s Equations of Motion
  • 9.7. Principle of Virtual Work
  • 9.8. Transformation to Generalized Coordinates
  • 9.9. Rayleigh’s Dissipation Function
  • 9.10. Hamilton’s Equations of Motion
  • 9.11. Cyclic Coordinates
  • 9.12. Lagrange’s Equations of Motion for a Continuum
  • 9.13. Hamilton’s Equations of Motion for a Continuum
  • 1 Oscillatory Phenomena
  • 1.1. Harmonic Motion
  • 1.2. Forced Oscillations
  • 1.3. Combination of Wave Forms
  • 1.4. Oscillations in Two Dimensions
  • 1.5. Coupled Oscillations
  • 1.6. Lagrange’s Equations of Motion
  • 1.7. Formulation of the Problem of Small Oscillations for Conservative Systems
  • 1.8. The Eigenvalue Equation
  • 1.9. Similarity Transformation and Normal Coordinates
  • 2 The Physics of Wave Propagation
  • 2.1. The Conservation Laws of Physics
  • 2.2. The Nature of Wave Propagation
  • 2.3. Discretization
  • 2.4. Sinusoidal Wave Propagation
  • 2.5. Derivation of the Wave Equation
  • 2.6. The Superposition Principle, Interference Phenomena
  • 2.7. Concluding Remarks
  • 3 Partial Differential Equations of Wave Propagation
  • 3.1. Wave Equation as an Equivalent First-Order System
  • 3.2. Method of Characteristics for a Single First-Order Quasilinear Partial Differential Equation
  • 3.3. Second-Order Quasilinear Partial Differential Equation

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