Courses Detail Information

ME6109J – Wave Propagation in Elastic Solids


Instructors:

Yanfeng Shen

Credits: 3 credits

Pre-requisites: This course will focus on conveying the fundamental concepts and theories of wave propagation. Although pre-requisite courses such as vibrations and elasticity are preferred, the instructor will carefully and systematically design the course material in the fashion of building blocks. The course is intended to be self-contained. Related fundamentals of elasticity and vibrations will be introduced in each topic to help the students pave their progress.

Description:

Solid wave phenomena are ubiquitous and are found in many engineering applications, such as
nondestructive evaluation (NDE), medical ultrasound imaging (including phased array ultrasound and
laser ultrasonics), transient analysis of biomechanical procedures, and earthquake engineering.
Emerging research/engineering topics such as ultrasonic/acoustic metamaterials and phononics may
also benefit from a thorough understanding of the wave mechanics.
Detailed topics: Formulation and solution of the wave propagation problem in an unbounded isotropic
medium. Study of the reflection-refraction, mode conversion problem at a plane interface. Discussion
of Rayleigh, Love, and general surface waves. Wave propagation in a bounded isotropic medium. Brief
touching of simulation techniques of wave procedures using analytical implementations, finite element
models, and finite difference technique. Engineering applications in Nondestructive Evaluation and
Structural Health Monitoring

Course Topics:

Introduction; wave equation; wave speed; D’ Alembert
Solution
Particle velocity; initial value problem; boundary value
problem
Wave reflection at free and fixed boundaries
Acoustic impedance; wave propagation through interfaces
Power and energy of generic waves; harmonic waves
Harmonic waves BVP; reflections; standing waves; power
and energy of harmonic waves
Flexural wave equation; review
Flexural wave harmonic solution; Flexural waves
dispersion;
Group velocity; energy velocity; demonstrations for wave
generation and reception
Navier Equation; plane waves in 3D solids
Pressure and shear waves
Harmonic plane waves in 3D; wave potentials
Z-invariant (plane strain) 3D waves; SH waves; P+SV
waves; review
Normal P-wave propagation through bi-material interface
Oblique SH wave propagation through bi-material
interface
Oblique P+SV wave propagation through biomaterial
interface; review
SH guided waves; dispersion curves; wave mode shapes
Lamb guided waves; dispersion curves
Lamb wave mode shapes; axial and flexural plate waves
Rayleigh guided waves;
Generic spherical and circular waves; review