Mathematics of wave propagation /
Julian L. Davis.
- 1 online resource (xv, 395 pages) : illustrations
Includes bibliographical references (pages 389-390) and index.
Physics of Propagating Waves Discrete Wave-Propagating Systems Approximation of Stress Wave Propagation in a Bar by a Finite System of Mass-Spring Models Limiting Form of a Continuous Bar Wave Equation for a Bar Transverse Oscillations of a String Speed of a Transverse Wave in a Siting Traveling Waves in General Sound Wave Propagation in a Tube Superposition Principle Sinusoidal Waves Interference Phenomena Reflection of Light Waves Reflection of Waves in a String Sound Waves Doppler Effect Dispersion and Group Velocity Partial Differential Equations of Wave Propagation Types of Partial Differential Equations Geometric Nature of the PDEs of Wave Phenomena Directional Derivatives Cauchy Initial Value Problem Parametric Representation Wave Equation Equivalent to Two First-Order PDEs Characteristic Equations for First-Order PDEs General Treatment of Linear PDEs by Characteristic Theory Another Method of Characteristics for Second-Order PDEs Geometric Interpretation of Quasilinear PDEs Integral Surfaces Nonlinear Case Canonical Form of a Second-Order PDE Riemann's Method of Integration Wave Equation One-Dimensional Wave Equation Factorization of the Wave Equation and Characteristic Curves Vibrating String as a Combined IV and B V Problem D'Alembert's Solution to the IV Problem Domain of Dependence and Range of Influence Cauchy IV Problem Revisited Solution of Wave Propagation Problems by Laplace Transforms Laplace Transforms Applications to the Wave Equation Nonhomogeneous Wave Equation Wave Propagation through Media with Different Velocities Electrical Transmission Line Wave Equation in two and Three Dimensions Two-Dimensional Wave Equation Reduced Wave Equation in Two Dimensions Eigenvalues Must Be Negative Rectangular Membrane Circular Membrane Three-Dimensional Wave Equation Wave Propagation in Fluids Inviscid Fluids Lagrangian Representation of One-Dimensional Compressible Gas Flow Eulerian Representation of a One-Dimensional Gas Solution by the Method of Characteristics: One-Dimensional Compressible Gas Two-Dimensional Steady Flow Bernoulli's Law Method of Characteristics Applied to Two-Dimensional Steady Flow Supersonic Velocity Potential Hodograph Transformation Shock Wave Phenomena Viscous Fluids Elementary Discussion of Viscosity Conservation Laws Boundary Conditions and Boundary Layer Energ Dissipation in a Viscous Fluid Wave Propagation in a Viscous Fluid Oscillating Body of Arbitrary Shape Similarity Considerations and Dimensionless Parameters; Reynolds'Law Poiseuille Flow Stokes'Flow Oseen Approximation Stress Waves in Elastic Solids Fundamentals of Elasticity Equations of Motion for the Stress Navier Equations of Motion for the Displacement Propagation of Plane Elastic Waves General Decomposition of Elastic Waves Characteristic Surfaces for Planar Waves Time-Harmonic Solutions and Reduced Wave Equations Spherically Symmetric Waves Longitudinal Waves in a Bar Curvilinear Orthogonal Coordinates Navier Equations in Cylindrical Coordinates Radially Symmetric Waves Waves Propagated Over the Surface of an Elastic Body Stress Waves in Viscoelastic Solids Internal Ftiction Discrete Viscoelastic Models Continuous Marwell Model Continuous Voigt Model Three-Dimensional VE Constitutive Equations Equations of Motion for a VE Material One-Dimensional Wave Propagation in VE Media Radially Symmetric Waves for a VE Bar ElectromechanicalAnalogy Wave Propagation in Thermoelastic Media Duhamel-Neumann Law Equations of Motion Plane Harmonic Waves Three-Dimensional Thermal Waves; Generalized Navier Equation Water Waves Irrotational, Incompressible, Inviscid Flow; Velocity Potential and Equipotential Surfaces Euler's Equations Two-Dimensional Fluid Flow Complec Variable Treatment Vortex Motion Small-Amplitude Gravity Waves Water Waves in a Straight Canal Kinematics of the Free Surface Vertical Acceleration Standing Waves Two-Dimensional Waves of Finite Depth Boundary Conditions Formulation of a Typical Surface Wave Problem Example of Instability Approximation Aeories Tidal Waves Variational Methods in Wave Propagation Introduction; Fermat's PKnciple Calculus of Variations; Euler's Equation Configuration Space Cnetic and Potential Eneigies Hamilton's Variational Principle PKnciple of Virtual Work Transformation to Generalized Coordinates Rayleigh's Dissipation Function Hamilton's Equations of Motion Cyclic Coordinates Hamilton-Jacobi Theory Extension of W to 2 n Degrees of Freedom H-J Aeory and Wave P[similar]vpagation Quantum Mechanics An Analog between Geometric Optics and Classical Mechanics Asymptotic Theory of Wave Propagation Principle of Least Action Chapter 1 3 -- 3 -- 4 -- 5 -- 5 -- 9 -- 10 -- 11 -- 16 -- 19 -- 19 -- 21 -- 25 -- 27 -- 29 -- 33 -- 36 -- Chapter 2 41 -- 41 -- 42 -- 42 -- 44 -- 49 -- 51 -- 55 -- 57 -- 61 -- 63 -- 65 -- 67 -- 70 -- 73 -- Chapter 3 85 -- Part I 85 -- 85 -- 90 -- 97 -- 101 -- 102 -- 105 -- 108 -- 111 -- 116 -- 120 -- 122 -- Part II 125 -- 125 -- 126 -- 127 -- 127 -- 131 -- 135 -- Chapter 4 145 -- Part I 145 -- 146 -- 149 -- 151 -- 157 -- 159 -- 161 -- 163 -- 163 -- 169 -- Part II 183 -- 183 -- 185 -- 190 -- 191 -- 193 -- 196 -- 197 -- 199 -- 201 -- 208 -- Chapter 5 213 -- 214 -- 223 -- 224 -- 227 -- 228 -- 229 -- 230 -- 232 -- 234 -- 237 -- 239 -- 240 -- 243 -- Chapter 6 250 -- 251 -- 252 -- 260 -- 263 -- 264 -- 265 -- 266 -- 270 -- 271 -- Chapter 7 282 -- 282 -- 285 -- 287 -- 293 -- Chapter 8 297 -- 297 -- 299 -- 300 -- 302 -- 309 -- 311 -- 311 -- 316 -- 317 -- 319 -- 321 -- 322 -- 324 -- 325 -- 327 -- 337 -- Chapter 9 344 -- 344 -- 345 -- 349 -- 350 -- 350 -- 352 -- 354 -- 357 -- 359 -- 362 -- 364 -- 370 -- 372 -- 376 -- 377 -- 380 -- Appendix 384.
Earthquakes, a plucked string, ocean waves crashing on the beach, the sound waves that allow us to recognize known voices. Waves are everywhere, and the propagation and classical properties of these apparently disparate phenomena can be described by the same mathematical methods: variational calculus, characteristics theory, and caustics. Taking a medium-by-medium approach, Julian Davis explains the mathematics needed to understand wave propagation in inviscid and viscous fluids, elastic solids, viscoelastic solids, and thermoelastic media, including hyperbolic partial differential equations and characteristics theory, which makes possible geometric solutions to nonlinear wave problems. The result is a clear and unified treatment of wave propagation that makes a diverse body of mathematics accessible to engineers, physicists, and applied mathematicians engaged in research on elasticity, aerodynamics, and fluid mechanics. This book will particularly appeal to those working across specializations and those who seek the truly interdisciplinary understanding necessary to fully grasp waves and their behavior. By proceeding from concrete phenomena (e.g., the Doppler effect, the motion of sinusoidal waves, energy dissipation in viscous fluids, thermal stress) rather than abstract mathematical principles, Davis also creates a one-stop reference that will be prized by students of continuum mechanics and by mathematicians needing information on the physics of waves.
9780691223377 0691223378
22573/ctv1826hdk JSTOR 9453275 IEEE
2021694870
Welle, ...
Wave-motion, Theory of. Th�eorie du mouvement ondulatoire. MATHEMATICS--Applied. Wave-motion, Theory of. Mathematische Physik Wellenausbreitung Welle WAVES. WAVE PROPAGATION. DIFFERENTIAL EQUATIONS. WAVE EQUATIONS. VISCOUS FLUIDS. Welle.