Courses:

Nonlinear Dynamics and Waves >> Content Detail



Syllabus



Syllabus



Course Outline




I. Introduction


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.



Homework


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.



Term Project


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.)



Exams


There will be one take-home mid-term exam. There will be no final exam.



Grading



ACTIVITIESPERCENTAGES
Homework40%
Mid-term exam30%
Term project30%



Textbook


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).


 








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