The following topics will be covered throughout the semester:
A. Sample Physical Origins of Wave Motion
- Taut String
- Elastic Rod
- Blood Flow in Arteries
- Sound in a Pipe
- Beam on an Elastic Foundation
- Traffic Flow on a Freeway
- Long Waves in Shallow Seas, Linearization
- Visit to the Nondestructive Evaluation Laboratory
B. One Dimensional Propagation
- General Solution, Branching of Arteries, Impedance
- Waves in an Infinite Domain, D'Alembert's Theory
- Characteristics
- Semi-infinite Domain and Reflection
- Forced Waves in an Infinite Domain
- String in an Elastic Surrounding, Dispersion
- Group Velocity and Energy Transport
- Transient Dispersion, Method of Stationary Phase
- Method of Stationary Phase (cont.)
- Scattering and Radiation of Harmonic Waves, Weak Scattering
- Strong Scattering of Long Water Waves by Depth Discontinuity
- Radiation Condition, Green's Function
- General Identities, Green Theorem
- Reflection in a Slowly Varying Medium, WKB Approximation
C. Two Dimensional Propagation
- Reflection and Transmission of Plane Waves at an Interface
- Angle of Incidence, Reflection Coefficient in the Complex Wave
- Elastic Wave in Solid, Governing Equations
- Free Waves in Infinite Space, Plane Elastic Waves
- Reflection of Elastic Waves from a Plane Boundary
- P and SV Waves
- SH Waves
- Scattering of SH Waves
- The Optical Theorem on Scattering
- Scattering of SH Waves by a Circular Cavity
- Diffraction of SH Waves by a Line Crack - Parabolic Approximation
- Rayleigh Surface Waves in a Half Space
- Elastics Waves due to a Line Load Traveling on The Ground Surface
- Supersonic, Transonic, and Subsonic
D. Waves in the Sea
- Linearized Equations
- Progressive Waves in Sea of Constant Depth. Dispersion and Flow Field. Particle Orbit and Energy Transport
- Wave Resistance of a Two Dimensional Obstacle
- Narrow Banded Dispersive Waves. The Schrodinger Equation for the Wave Envelope
- Radiation of Surface Waves Forced by an Oscillating Line Pressure on the Surface
- Kelvin Ship Waves
- Internal Waves in a Stratified Fluid. Dispersion Relation
- Internal Waves in an Unbounded Fluid, St. Andrew's Cross
E. Dispersive Waves in Random Media
Depending on class interest and time we may discuss:
F. Waves through Laminated Media
- Effective Equation for Thin Laminates
- Effective Equation for Thick Laminates
or
G. Nonlinear Waves
- Traffic Waves. Green and Red Lights
- Shocks and Traffic Jam
- Bores and Hydraulic Jumps
- Bore from the Breaking of a Dam