Wave Propagation in Solids

INSTRUCTOR: | Ronald D. Kriz ( rkriz@vt.edu) |
---|---|

Office Hours |
Times other than regular office hours by appointment only; contact email: rkriz@vt.edu, the day before or sooner. See instructor for special arrangements. |

Text |
Class Notes. References listed below |

Prerequisite |
Continuum Mechanics, ESM 5014 |

Letter Grades |
A:93-100; A-:90-92; B+:87-89; B:83-86; B-:80-89; C+:77-79; C:73-76; C-:70-72; D+:67-69; D:63-66; D-:60-62; F:59 -> |

**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.

- 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

- A. Rods.

- J.W.S. Rayleigh,
*The Theory of Sound*, Vols. 1 and 2, Dover Publications, New York, 1945. - L. Brillouin,
*Wave Propagation in Periodic Structures*, Dover Publications, New York, 1946. - H. Lamb,
*The Dynamical Theory of Sound*, Dover Publications New York, 1960. - H. Kolsky,
*Stress Waves in Solids*, Dover Publications, 1963. - F.I. Fedorov,
*Theory of Elastic Waves in Crystals*, Plenum Press, New York, 1968. - M.J.P. Musgrave,
*Crystal Acoustics*, Holden-Day, San Franscisco, 1970. - 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. - B.A. Auld,
*Acoustic Fields and Waves in Solids*, Vols. I and II, John Wiley and Sons, 1973. - L.M. Brekhovskikh,
*Waves in Layer Media*, Academic Press Inc., New York, 1980. - J.D. Achenbach,
*Wave Propagation in Elastic Solids, North-Holland*, 1987,

Ronald D. Kriz

Virginia Tech

College of Engineering

**ESM 5344 Wave Propagation in Solids
**

Current: http://www.esm.rkriz.net/classes/ESM5344/ESM5344_NoteBook/ESM5344_Gen.html

Original: http://www.esm.vt.edu/~rkriz/classes/ESM5344/ESM5344_NoteBook/ESM5344_Gen.html