主题目录

    • University:  Massachusetts Institute of Technology 

      Instructors:   Prof. Triantaphyllos Akylas

      Course Number:  18.377J

      Level:  Graduate

      Course Description

      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.

  • 教学大纲(Syllabus)

    Course Meeting Times

    Lectures: 2 session / week, 1.5 hours / session

    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
    Homework 40%
    Mid-term exam 30%
    Term project 30%

    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).

  • 其他教学资源(Other Resources)

    • Readings

      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.

       Minorsky, Nicholas. Nonlinear Oscillations. Melbourne, FL: Krieger Publishing, 1974. ISBN: 9780882751863.

       Nayfeh, Ali Hasan, and Dean T. Mook. Nonlinear Oscillations. New York, NY: John Wiley & Sons, 1995. ISBN: 9780471121428.

       Stoker, J. J. Nonlinear Vibrations in Mechanical and Electrical Systems. New York, NY: John Wiley & Sons, 1992. ISBN: 9780471570332.

       Den Hartog, J. P. Mechanical Vibrations. Mineola, NY: Dover Publications, 1985. ISBN: 9780486647852.

       Andronov, A. A., A. A. Vitt, and S. E. Khaikin. Theory of Oscillators. Mineola, NY: Dover Publications, 1987. ISBN: 9780486655086.

       Hayashi, Chihiro. Nonlinear Oscillations in Physical Systems. Princeton, NJ: Princeton University Press, 1986. ISBN: 9780691083834.

       Pippard, A. B. Response and Stability: An Introduction to the Physical Theory. Cambridge, UK: Cambridge University Press, 1985. ISBN: 9780521319942.

       Strogatz, Steven H. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering. New York, NY: Perseus Books, 2001. ISBN: 9780738204536.

       Iooss, Gerard, and Daniel D. Joseph. Elementary Stability and Bifurcation Theory. New York, NY: Springer, 2004. ISBN: 9780387970684.

       Whitham, G. B. Linear and Nonlinear Waves. New York, NY: John Wiley & Sons, 2006. ISBN: 9780471359425.

       Craik, Alex D. D. Wave Interactions and Fluid Flows. Cambridge, UK: Cambridge University Press, 1999. ISBN: 9780521368292.

       Drazin, P. G. Nonlinear Systems. Cambridge, UK: Cambridge University Press, 1992. ISBN: 9780521404891.

       Newell, Alan C. Solitons in Mathematics and Physics. Philadelphia, PA: Society for Industrial and Applied Mathematics, 1987. ISBN: 9780898711967.

       Dauxois, Thierry, and Michel Peyrard. Physics of Solitons. Cambridge, UK: Cambridge University Press, 2006. ISBN: 9780521854214.