--------------------------------- README ----------------------------------------

Summary of FEM simulations of wave propagation flux deviations in unidirectional
Graphite/Epoxy at various fiber orientations from 0 to 90 degrees (0-90) from the
vertical axis (red line). Results summarized in composite images (*.jpg) and also 
animations (*.mov). These simulations can be reproduced by students in ESM5344 by 
selecting the web link "Small FEM mesh (30x60): Access Simulation" web page URL:
http://www.sv.vt.edu/classes/ESM5344/ESM5344_kriz_NoteBook/ESM5344_kriz.html .
Individual animations archived as animated-gifs and quick-time format in 
directories:

          Directory name                   description

       wave2d30x60_0-90_QL+XX   transmitter generates only QT waves
       wave2d30x60_0-90_QT-XX   transmitter generates only QL waves
       wave2d30x60_0-90__L      transmitter vibrates pure longitudinal
       wave2d30x60_0-90__T      transmitter vibrates pure transverse

The objective of these simulations is to demonstrate how anisotropy (fiber
orientation) influences wave type (L,T,QL,QT) and energy flux deviation.
Wave type can also be controlled by transmission of energy at the simulated
transducer (transmitter) boundary. Results are summarized in *.jpg images.
Labels L,T,QL,and QT indicate transducer boundary vibration directions:
L indicates longitudinal vibration parallel to the vertical axis (red line),
T indicates transverse vibration perpendicular to the vertical axis, QL and
QT indicates vibration directions predicted as eigenvector solutions to
Christofell's equation. For a prescribed direction to the plane wave shown
as the vertical red line, both eigenvalues (wave speeds) and eigenvectors
(wave vibration directions) are functions ONLY of the fourth order stiffness
tensor, Cijkl.

Directories labeled QT AND QL archive simulations that preferentially launch QT 
and QL waves with simulated transducers. Listed below are vibration displacement 
vibration orientations (angles, degrees) of QL and QT waves propagating through 
unidirectional Graphite/Epoxy at fiber orientations between 0 and 90 degrees.

Fiber Orientation, (-)      QL eigenvector angle        QT eigenvector angle
  clockwise from the    (+) counterclockwise from      (-) clockwise from the
 vertical (red) axis,  the horizontal (green) axes,   horizontal (green) axes,
     (degrees)                  (degrees)                   (degrees)

       -12                        +79.0                       -11.0
       -21                        +70.8                       -19.2
       -30                        +62.8                       -27.2
       -39                        +54.9                       -35.1
       -51                        +45.2                       -44.8
       -60                        +39.2                       -50.8
       -69                        +37.3                       -52.7
       -81                        +75.0                       -15.0

Angles calculated as eigenvector solutions to Christoffel's equation given the
Graphite/Epoxy fourth order stiffness tensor, Cijkl, and density. Calculation
results between 0 and 90 degrees summarized in QT-QL_EigenVectors.txt