Offered Spring, Odd Years

Credit Hours: 3-0-3
Catalog Description: Wave motion in solids, wave equations, analytical and numerical solutions, ultrasonic NDE.
Textbooks: J.D. Achenbach, Wave Propagation in Elastic Solids, 1st Edition, Elsevier Science, 1984
Instructors: Jiamin Qu, Yves Berthelot, Jerry Ginsberg, Peter Rogers
Goals: The goal is to introduce the fundamental principles governing wave motions in solids. Students will be exposed to the mathematical formulations of the governing equations of wave motion, analytical and numerical techniques of solving these equations, as well as the applications of ultrasonics to quantitative nondestructive evaluation.
Audience: Graduate students in ME, AE, CE and MSE.
  • Introduction to 1-D Wave Motion
    • Motion and deformation
    • Time rate of change
    • Conservation of mass and balance of momentum
    • Time harmonic wave and its energy flux
  • Fundamental Equations of 3D Linear Elasticity
    • Kinematics and dynamics
    • Stresses, strains and their relationship
    • Equations of equilibrium
    • Initial and boundary conditions
    • Hamilton's principle
    • Displacement potentials
  • Elastodynamics Theories
    • Reciprocity relations
    • Scalar and vector potentials
    • Helmholtz decomposition
    • Basic singular solutions in elastodynamics
    • Integral representations
  • Waves in an Unbounded Medium
    • Spherical and plane waves
    • Slowness diagram
    • Propagation of wave front
  • Harmonic Waves in Layered Media
    • Reflection and transmission
    • Rayleigh and Stoneley Waves
    • Guided waves
  • Transient Waves
    • Lamb's problem
    • Transient motion in a layer
    • Impact of a rod
  • Scattering of Elastic Waves
    • Cylindrical and spherical inclusions
    • Cracks
  • Asymptotic Methods
    • Asymptotic expansion of integrals
    • Born approximation
    • Ray method
    • Matched Asymptotic method