ME 431

ME 4600-431: Mechanical Vibrations


Professor: Dr. Dane Quinn ()
Lectures: 4600:431-002 M,W,F 9:55am-10:45am; Whitby 210.
Office Hours: tbd
Text: B. Balachandran and E. B. Magrab
Thomson-Engineering, 2004.
ISBN: 0534395104

Communication Center File No. 394
TA: Jason Miller ()
Office Hours: tba

Homework: 10%
Quiz: 10%
Exams: 40%
Final: 25%
Project: 15%

  1. Introduction and Background
    1. A Description of Harmonic Motion
    2. Spring-mass Model---An Overview
  2. Newtonian Mechanics
    1. Linear Momentum Balance
    2. Angular Momentum Balance
    3. Kinematics
  3. Fundamentals of Mechanical Systems
    1. Equilibrium Points
    2. Linearization
    3. Elasticity
      • Constitutive Modeling
      • Potential Energy
      • Structural Elements
    4. Dissipative Forces
    5. Equivalent Systems
  4. Elements of Vibrating Systems
    1. Elasticity/Springs
    2. Viscous Dampers
  5. Free Vibrations of One-Degree-of-Freedom Systems
    1. Modeling
    2. Undamped Systems
    3. Damped Systems
  6. Harmonic Excitation of One-Degree-of-Freedom Systems
    1. Harmonic Forcing
    2. Displacement Excitation
  7. Multi-Degree-of-Freedom 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 not be accepted beyond one additional class period:
Classes Late Percent Off
1 10%
2+ not accepted
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.

Quiz Quizes will be held weekly. Each will be composed of a single problem taken directly from the homework of the previous week. My goal is to motivate you to not only do the homework but to review the solutions once they are made available.

Exams and Final: There will be two exams during the semester. Each will be closed book but I will provide brief notes.
Note: The final will be comprehensive.

Project Students, in groups of no more than three, are to choose an appropriate physical system to model and analyze using the tools and techniques learned in this class, and it is expected that students will use both analytical design tools as well as numerical methods to aid in their design and analysis.

References Dynamics:
  • Beer, F. P., and Johnston, Jr., E. R., Vector Mechanics for Engineers: Dynamics; 6th ed., McGraw-Hill, Boston, 1997.
  • McGill, D. J., and King, W. W., Engineering Mechanics, an Introduction to Dynamics; 3rd ed., PWS Publishing, Boston, 1995.
  • Meriam, J. L., and Kraige, L. G., Engineering Mechanics; 4th ed., John Wiley & Sons, New York, 1997.
  • Shames, I. H., Engineering Mechanics. Dynamics; 4th ed., Prentice-Hall, New Jersey, 1997.
Engineering Vibrations:
  • Inman, D. J., Engineering Vibration; Prentice-Hall, New Jersey, 1996.
  • Kelly, S. G., Fundamentals of Mechanical Vibrations; McGraw-Hill, New York, 1993.
  • Rao, S. S., Mechanical Vibrations; 3rd ed., Addison-Wesley, Massachusetts, 1995.
  • Thomson, W. T., and Dahleh, M. D., Theory of Vibration with Applications; 5th ed., Prentice-Hall, New Jersey, 1998.
  • Tongue, B. H., Principles of Vibration; Oxford University Press, New York, 1996.

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