ME 863:  Nonlinear Oscillations Spring 2002

INSTRUCTOR:

Brian Feeny
2328-C EB, 353-9451, 353-1750 fax
feeny@me.msu.edu
MAIN REFERENCES:
Nonlinear Oscillations
A. H. Nayfeh and D. T. Mook
Wiley-Interscience, 1979

Lecture Notes on Nonlinear Vibrations
R. H. Rand
http://www.tam.cornell.edu/
GRADING:
50% Homework
25% Midterm exam
25% Final Exam
LECTURE: 2:40-4:00 Tu Th, 004 UP

OFFICE HOURS: TBA

PHENOMENA (See the course outline):

Local stability
Frequency dependent on amplitude
Limit cycles, relaxation oscillations, stick-slip
Forced Vibration
nonlinear resonance
jump phenomena
primary and secondary resonances
Parametric excitation
Internal resonance in multi-degree-of-freedom systems
METHODS:
Linearization
Qualitative methods--phase portraits, Poincaré-Bendixson
Perturbations--Linstedt's method, multiple scales, averaging
Harmonic balance
Floquet theory
POLICIES: Text: There is no required text. However, there are a number of good references available if you wish to buy a book.

Homework: Talk to anybody. Refer to any book. Write your own solutions, and cite your references. Student collaboration on the homeworks is encouraged, but no copying. Copying is plagiarism, and there is a departmental policy on plagiarism.

Exams: In-class exams will be open-notes. You may develop your notes to whatever extent you wish. Take home exams are not likely, but in such case you must work alone on take-home exams. Talk only to the instructor. Refer to books as allowed. Write your own exam and cite your references. Make-up exams will be given only in the case of documented emergencies.

 TOOLS: Numerical simulation will be required in some homeworks. Computer algebra
is helpful but not required. Matlab and Mathematica are available in DECS.