Phys 598 EW Elastic Waves Fall 2015
Instructor: Prof Richard Weaver OFFICE HOURS: Tuesdays 1-3 pm (begin 9/1/5)
4115
ESB 333-3656
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Standard texts
and monographs, all with a view towards solving classical problems in elastic
wave propagation:
K.
F. Graff, "Wave Motion in
Elastic Solids," Dover , NY
1975 (inexpensive!)
J.D.
Achenbach, "Wave Propagation
in Elastic Solids,
NorthHolland/Elsevier
Emphasis
on exact solutions for unbounded and simply bounded media
R.
Truell, C. Elbaum and B. Chick, "Ultrasonic methods in solid state
physics,"
Emphasis on ultrasonics in unbounded media and half spaces.
J.
Miklowitz "Theory of elastic waves and waveguides" 1978
Waveguides:
Plates and rods
Y-H
Pao and C C Mow "Diffraction of Elastic Waves and Dynamic Stress
Concentrations" Rand Corp. 1973.
Emphasis on scattering in simple geometries
K. Aki
and P.G. Richards, "Quantitative Seismology,"
High level; Attention confined to 3-d, with emphasis on
applications in
seismology.
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Course will
meet twice a week M W 11:00 Ð 12:20. Grade will be based on weekly (occasionally
twice weekly?) HW assignments and class participation, and on a final exam.
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Schedule
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Wednesday
8/26 |
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Monday 8/31 |
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Wednesday
9/02 |
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Monday 9/07 |
Labor Day,
no class |
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Wednesday
9/09 |
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Monday 9/14 |
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Wednesday
9/16 |
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Monday 9/21 |
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Monday 9/28 |
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Wednesday
9/30 |
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Wednesday
10/07 |
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Monday 10/12 |
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Wednesday
10/14 |
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Monday 10/19 |
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Wednesday
10/21 |
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Monday 10/26 |
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Wednesday
10/28 |
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Wednesday
11/04 |
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Monday 11/09 |
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Wednesday
11/11 |
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Monday 11/16 |
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Wednesday
11/18 |
HW12 due (on Friday) |
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Monday 11/23 |
Fall Break |
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Wednesday
11/25 |
Fall Break |
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Monday 11/30 |
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Wednesday
12/02 |
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Monday 12/07 |
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Wednesday
12/09 |
Final exam = HW15 due by 4:30 Th Dec 17
Tentative
course outline:
I. Graff 5.1.1 Review of linear elasticity -
Stress, strain, traction, constitutive
laws, Boundary Conditions
Balance of Momentum -
Displacement Equation of Motion - energy balance
Lagrangian re-formulation
Helmholtz
Decomposition of displacement field, displacement potentials
5.1.2
Alternate forms for Equation of motion
5.1.3 Plane
Waves of P & S type
Visco-Elastic Constitutive relations,
Attenuation & Dispersion of Plane waves
II. Governing Equations (often approximate)
in reduced dimensions
2-d
Plane
strain SH and P-SV
Plane
stress extensional waves in thin plates
SH
waves in thin (or thick) plates
Bending
waves in thin plates, Kirchoff plate theory.
1d
Torsional
waves in circular rods
Bending
waves in beams, Euler-Bernoulli theory
Extensional
waves in rods
Strings
derivation
of linearized equation
III Applications in reduced dimensions, Exercises in Fourier Transforms and
Greens functions and scattering.
A. 1-d several mathematical
exercises on (Graff Chapters1,2
and 3)
scattering,
dispersion and responses of strings.
B. Kirchoff plates Graff Chapter 4
Free Vibration
plane waves
circular
crested waves
Harmonic waves
& Dispersion relations
for Cartesian
and Polar
co-ordinates
The Infinite
stiff ribbon, a Multi branched dispersion relation
Finite
systems, normal modes
Forced Vibration; Greens
functions
Infinite
plates, Triple FT's, & Hankel Transforms
Infinite
ribbon
Finite systems
IV
Elastodynamics in 3 dimensions 5
weeks
The Fundamental solution, the Green's Dyadic in unbounded 3-d media (Graff
5.2.3 )
=>
in k,w Fourier Transform space
=> as a function of r and w, the "harmonic G's Dyadic" -
Energy
Flow for Harmonic Solution
in the
time domain, as a function of r &
t
Strain
Nuclei sources
Solutions
in Half Spaces
Free vibration: (Graff
6.1 )
P/SV and SH Reflections, Mode Conversions,
Snell's law, Critical angles
Rayleigh
Surface Waves
Other
boundary conditions
Layered
Half space - Love Waves
Forced
problems
6.2 SH
sources in Half spaces
6.3 P/SV sources in half spaces
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Line
sources and point sources; Lamb's Problem; Cagniard Method,
other
sources in half spaces.
6.4 Free vibrations in Joined
Half spaces, especially fluid/solid case
Reflections,
Transmissions, Surface waves, Leaky Surface waves
V. Elastic waveguides
Graff 8. Rayleigh-Lamb Waves in a
Plate
Pochammer
waves in a rod
Responses
in Waveguides: Green's functions in an isotropic plate:
Normal
Mode Solution, Ray Theory Solution, Numerical Inversion
VI
Statistics of elastic waves in irregular reverberant bodies.
Multiple
scattering in random media -
average G, and effective maedium
Diffuse
field assumption and its justification.
Consequences
Universal
Partition, surface/bulk and P/S and H/V.
Diffusion
of multiply scattered wave energy
Enhanced
backscatter
Field
correlations = Greens function.
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