University： Massachusetts Institute of Technology
Instructors: Prof. Triantaphyllos Akylas
Course Number: 18.377J
This graduate-level course provides a unified treatment of nonlinear oscillations and wave phenomena with applications to mechanical, optical, geophysical, fluid, electrical and flow-structure interaction problems.
Course Meeting Times
Lectures: 2 session / week, 1.5 hours / session
Course organization, scope. Typical examples of nonlinearities in vibration and wave phenomena.
II. Nonlinear Vibrations
Review of phase plane for one-d.o.f. systems, limit cycles. Perturbation techniques for weakly nonlinear systems. Nonlinear forced vibrations; jump phenomena, synchronization, superharmonic and subharmonic resonance. Extensions to multi-d.o.f. and continuous systems. Examples and applications.
III. Nonlinear Stability and Bifurcation
Weakly nonlinear approaches. Techniques for computing bifurcating nonlinear-response branches. Examples and applications.
IV. Nonlinear Waves
Nonlinear dispersion relation and finite-amplitude periodic waves. Propagation of nonlinear pulses and the nonlinear Schrödinger equation. Long-crested waves and the Korteweg-de Vries equation. Nonlinear wave interactions. Forced nonlinear waves. Examples and applications.
There will be 5 problem sets; typically, a new problem set will be given and you will have two weeks to work on it. Some problems will require the use of a computer, and familiarity with MATLAB® would be helpful. Each student is expected to work on the homework problems independently; no collaboration with others is allowed.
Each student will study and review critically at least one published research paper on a topic of his/her choice in the general area of nonlinear dynamics and waves. (A list of sample topics will be distributed later.)
There will be one take-home mid-term exam. There will be no final exam.
Grading criteria. ACTIVITIES PERCENTAGES Homework 40% Mid-term exam 30% Term project 30%
The subject will be based on the material presented in the lectures. There is no required textbook. A general list of references will be provided (if you need additional references for a particular topic, please feel free to ask the instructor).
The subject will be based on the material presented in the lectures. There is no required textbook. A general list of references is provided here.