WEIGHTING: 20% homework, 30% tests/midterm, 30% final exam and 20% class project. When justified, these weights may be altered to the student's benefit, e.g. homework missed due to major illness, death in immediate family, etc.

TESTS/MIDTERM: Typically there are two 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: 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. Homework problems are typically assigned once a week, and typically due one week after they are assigned. Because some homework assignments are more difficult than others, a weight is assigned for each problem. Assignments will be discussed in class. No homework will be accepted late unless you can provide documentation of an illness or other unusual circumstance.

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, Spring Semester. Posted here is an example of a Student Class Project. Since the class project is assigned the same 20% as homework, time spent on project is expected to be equivalent to time spent on homework. Under special circumstances the class project percentage can be negotiated with instructor.

HONOR CODE: The Virginia Tech Honor code applies to all homework and exams, and no form of dishonesty will be tolerated. 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 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,