ME 630

ME 4600-630: Vibrations: Discrete Systems


Professor: Dr. Dane Quinn ()
Lectures: 4600:630-080 T, Th 6:40-7:55pm; MGH 304.
Office Hours: TBA

L. Meirovitch,
Principles and Techniques of Vibrations;
Prentice Hall, New Jersey, 1997.

C. Lanczos,
The Variational Principles of Mechanics;
Dover Publications, Inc., New York, 1986.

Homework: 20%
Exams: 50%
Final: 30%

  1. Introduction and Background
  2. Newtonian Dynamics
  3. Analytical Mechanics
    1. Calculus of Variations
    2. The principle of Virtual Work
    3. D'Alembert's Principle
    4. The Lagrangian Equations of Motion
  4. Single-degree-of-freedom Linear Systems
    1. Free Vibrations
    2. Forced Vibrations
  5. Multi-degree-of-freedom Linear Systems
    1. Existence and Stability of Equilibrium Points
    2. Linearization About Equilibrium Points
    3. Free Vibrations
    4. Forced Vibrations
  6. Eigenvalue Problems
  7. Computational Techniques
  8. Qualitative Analysis of Dynamical Systems

Office Hours Office hours will be held in the respective offices unless noted at some later time (if, say, the offices become overcrowded I'll try to find a new location). Office hours are an opportunity for you to get extra help, clarify a mistake, work problems, etc. However you must come prepared. Don't walk in and ask us to teach you ``stuff''. Come with specific problems to be worked or specific ideas you don't understand. If you can not make it to one of the scheduled office hours then feel free to drop by and if I have time I'll be glad to help you, but be prepared to schedule a convenient time for us both.

Homework Homework will be collected during class and (hopefully) returned the following week. You may work together on homework but any and all collaboration must be CLEARLY NOTED (this includes any sources used other than your text and own notes). In addition you must write up your own work. Please work neatly, show all necessary steps (I don't need to see that 2+2=4), and box in your final answer.

Late Homework Policy:

Late homework will be marked as follows:
Classes Late Percent Off
1 5%
2+ +10% per class
Because the homework is graded mostly on effort (rather than correctness), I feel that this policy strikes a good balance between flexibility with respect to your time and the necessity of staying current in class.

Exams and Final: There will be two exams during the semester. Each will be closed book but I will allow one page (front and back) of notes.
Note: The final will be comprehensive.

Etc.: I hope that you enjoy the class. If there is anything that I can do to help you please let me know.