MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
Department of Mechanical
Engineering
1.138J/2.062J/18.376J
Wave Propagation
Spring 2012
Course Outline | References | Lecture Notes | Problem Sets | Solutions | Quiz
I. Sample wave problems and elementary concepts
Taut string, elastic rod
Shallow-water waves, acoustic waves in a pipe
Traffic flow, blood flow in arteries
Exponential notation, frequency, wave number, phase velocity, etc.
II. One-dimensional propagation
The wave equation: transient responses, characteristics
Dispersion: rod on elastic foundation, flexural waves in a beam
Group velocity: dispersion of transient waves, stationary phase
Group velocity and energy transport
Scattering of harmonic waves, radiation condition
III. Two-dimensional propagation
Plane waves, sound in homogeneous fluids
Nearly plane waves, geometrical acoustics
P, SV and SH waves in elastic solids
Rayleigh waves in half space, Love waves in a layered medium
Reflection and refraction from a plane interface, mode conversion
Scattering of elastic waves, diffraction, parabolic approximation
Waves in an elastic layer
IV. Free-surface and internal gravity waves in fluids
Free-surface waves: dispersion relation, group velocity, phase velocity
Waves in a current, ship waves
Transients due to impulsive forcing
Internal waves in a stratified fluid, anisotropic wave propagation
Modes in a stratified fluid layer
V. Waves in periodic media
Bloch–Floquet theory
Stop bands, pass bands
Bragg resonance