Department of Applied Science
4355/5355 Elastic Wave Theory
I. Instructor: Dr. Haydar Al-Shukri
II. Catalog Description:
Elasticity theory developed as a basic necessity to the theory of seismology. Analysis of stress and infinitesimal strain. Perfect elasticity. Equation of motion in term of displacement. Vibration and waves. Theories of body and surface waves.
III. Prerequisites: Calculus I, II, III, Differential Equation
IV. Course Objectives:
A. To give the graduate student of applied sciences the necessary theoretical background in elasticity and the stress-strain relation.
B. Introduce the participants to the basic theory of elastic waves and the derivation of equation of motion.
C. Provide the student with a theoretical background about body waves and surface waves excitation and propagation in elastic media.
D. Introduce the student to the ray theory and energy partition.
V. Expectation of Students:
A. Enrollees will participate in all class meeting and will complete assigned readings and other preparation to discussions of the subject matter. Graduate students will be required to complete a number of additional class assignments.
B. Enrollees will achieve satisfactory grades on a midterm and final exams.
C. Graduate students are expected to complete a comprehensive term paper about a relevant topic approved by the instructor. They are also expected to perform one-hour presentation regarding their research.
VI. Course Content:
1. Analysis of stress
2. Infinitesimal strain
3. Perfect elasticity
4. Equation of motion
B. Vibration and waves
1. Vibration of systems with one degree of freedom
2. Wave equation
3. Solution to the wave equation (Cartesian; spherical; cylindrical)
4. Solution in horizontally layered media
C. Body elastic waves
1. Compressional (P) and Shear waves (S)
2. Form of ground motion in an earthquake
D. Surface waves
1. Rayleigh waves
2. Love waves
3. Surface waves dispersion
4. Group and phase velocity
E. Midterm Examination.
F. Reflection and refraction of plane waves
1. Solution for the case of two media
2. Energy balance equation
3. Computation of dispersion curves in multi-layered media
G. Ray theory
1. Wavefronts and Eikonal equation
2. Properties and equation of ray
3. Travel-time and horizontal range
4. Spherically stratified model
H. Final examination or oral presentation of term paper.
VII. Basis for student evaluation:
1. Midterm Examination 25%
2. Assignments 25%
3. Term paper and presentation 25%
4. Final Examination 25%
B. Undergraduate Students:
2. Assignments 33%
3. Final examination 34%