WEIGHTING: 20% homework, 30% tests/midterm, 30% final exam and 20% class project. When appropriate, these weights may be altered to the student's benefit to handle substantial improvement near the end of the course, homework missed due to major illness, etc.

FINAL EXAM: (14T) May 13, 1:05-3:05 pm, Randolph 220

TESTS/MIDTERM: Typically there are three tests or one-midterm exam. Absence during a test will result in a grade of zero. Makeup tests will be given only where a very serious documented reason exists for absence.

HOMEWORK: Homework problems are due once a week, one week after they are assigned. Assignments will be given in class. No homework will be accepted late for any reason whatsoever. Each assignment will be given a percentage grade based on equal weight for each problem in the assignment. If you fail to hand in more than one assignment due to major illness or other unusual circumstance, please provide a note of explanation and attach any available supporting documentation. Please leave flat and staple upper left corner. Put your name in the upper right corner, the assignment number and date in the upper left corner.

CLASS PROJECT: The class project will consist of a written report on some topic dealing with wave propagation in solids. The subject is completely up to the student and can deviate significantly from the course outline. Topic should be choosen, with the instructor's approval, due mid-March, 2009.

HONOR CODE: The Virginia Tech Honor code applies to all homework and exams, and no form of dishonesty will be tolerated by the instructor or the students. If a serious attempt to work a homework problem is unsuccessful, then help may be sought from another student, including those currently in the course. But this help must be limited to the minimum necessary to allow further progress. Copying of another students work, including work from old notes, or permitting your work to be copied, is considered a serious breach of the honor code.

Outline:

• I. Formulation of Elastodynamics
  • A. Mathematical Preliminaries
  • B. Equation of Motion in a Continuum
  • C. Definition of a Plane Wave

• II. Wave Propagation in Elastic Anisotropic Medium
  • A. Solution to Wave Equation for Infinite Medium
  • B. Energy Flux
  • C. Wave Surfaces: phase velocities, group velocities, slowness, and energy
  • D. Acousto-Elastic effect of Stress induced anisotropy

• III. Wave Propagation in Elastic Isotropic Medium
  • A. Solution to Wave Equation for Infinite Medium.
  • B. Reflection at a Plane Stress-Free Boundary
    • 1. Incident Longitudinal Mode
    • 2. Incident Transverse Mode
      • a. Particle Displacements Parallel to Boundary
      • b. Particle Displacements in Incident Plane

  • C. Rayleigh Wave and Other Surface Waves
  • D. Critical Angle Phenomena
  • E. Extension of Reflection Problem to Interface Between Two Media
  • F. Love Waves, Stonely Waves
  • G. Internal Conical Refraction

• IV. Wave Propagation in Bounded Media
  • A. Rods.
    • 1. One Dimensional Model
    • 2. Pochhammer-Chree Model
    • 3. Concentric Cylinders

References:

1. J.W.S. Rayleigh, The Theory of Sound, Vols. 1 and 2, Dover Publications, New York, 1945.

2. L. Brillouin, Wave Propagation in Periodic Structures, Dover Publications, New York, 1946.

3. H. Lamb, The Dynamical Theory of Sound, Dover Publications New York, 1960.

4. H. Kolsky, Stress Waves in Solids, Dover Publications, 1963.

5. F.I. Fedorov, Theory of Elastic Waves in Crystals, Plenum Press, New York, 1968.

6. M.J.P. Musgrave, Crystal Acoustics, Holden-Day, San Franscisco, 1970.

7. R.E. Green, Jr., "Ultrasonic Investigation of Mechanical Properties," Treatise on Materials Science and Technology, Vol. 13, H. Herman, Ed., Academic Press,Inc., New York, 1973.

8. B.A. Auld, Acoustic Fields and Waves in Solids, Vols. I and II, John Wiley and Sons, 1973.

9. L.M. Brekhovskikh, Waves in Layer Media, Academic Press Inc., New York, 1980.

10. J.D. Achenbach, Wave Propagation in Elastic Solids, North-Holland, 1987,