Instructor:               Professor Pan Michaleris
                              232 Reber Bldg
                              863-7273
                             pxm32@psu.edu
                              Office hours: Monday & Wednesday: 1:30-3:00 p.m.

Teaching Assistant:  Ming-Chang Pai
                              Room 220, Desk 37, Reber building
                              863-0592
                             mxp157@psu.edu
                              Office hours: Tuesday & Thursday  1:00-2:30 p.m.

Text:               Mechanical Vibrations by S.S Rao, 2nd and 3rd Edition.
Addl. Text:      Theory of Vibration with Applications by W.T Thompson an M.D. Dahleh, 5th Edition

Prerequisites:  Math 220, and 251, E Mech 12 and 13, ME 50 

   Homework      25% (drop the worst)
   Projects           10%
   Midterms         40%
   Final                25%

The course deals with determining the response of mechanical systems to time varying disturbances such as forces, moments, displacements, etc.  The response is expressed in terms of varying displacements or stresses.  The mechanical systems are represented (modeled) as combinations of energy storage and energy dissipative components such as springs, masses and dampers.  Typical examples/applications of such systems include: car suspensions, aircraft landing gears, ship propulsion systems, machine tool drives, etc.

The course utilizes mathematical techniques covered in earlier mathematics courses such as ordinary differential equations with constant coefficients, Fourier analysis, Laplace transforms and the convolution integral.  We will utilize computers where appropriate to facilitate solutions of more complex problems.

• Class attendance is highly recommended as material is frequently presented which departs from the text.
• We will solve example problems in the course of the lectures
• Homework problems will be assigned approximately every Friday and will be due one week later.
• There will be two mid-term examinations.
• We will assign one lab and one computer project.  These projects will be collected for grading.
• Absolutely no late homework will be accepted.
• Consulting/studying in teams is encouraged.  However, each team member must work on all parts of the homework and projects and must hand in their own individual work.
• All exams will closed book.  However, you may bring with you up to six pages of notes.
• Academic dishonesty, including but not limited to copying from other students during exams and quizzes, photocopying of computer problems and copying of computer data files, will not be tolerated and will be prosecuted vigorously through the university judicial system.

This is a tentative schedule and it should be used only as a guideline.  This schedule may be changed and it is the student’s responsibility to be aware of any changes, which will be announced in the class.

Date  Reading  Topic     Reading Problems
W 8/26  1.1-6  Introduction, Concepts
F 8/28  1.7-10  Elements of Vibratory Systems  1.1,2,4,5,12,13
M 8/31  2.1-2  Equations of Motion, Newton’s Laws 1.19,24,25,28,29
W 9/2  notes  Energy Methods
F 9/4  notes  Differential Equations Review
M 9/7    no class
W 9/9  2.3-4  Free Vibration of Undamped SDOF’s 2.1,4,5,6,8
F 9/11  2.5  Free Vibration of Undamped SDOF’s 2.11,12,13-16,19,24,27,28
M  9/14  2.6-7  Free Vibration of Damped SDOF’s  2.49,52,55,60,62,79-84,97
W  9/16  3.1-3  Forced Vibration of Undamped SDOF’s 3.1,2,6
F 9/18  3.4-5  Forced Vibration of Damped SDOF’s 3.7,8-11,15-18
M 9/21  3.6  Base Excitation    3.21,22,24, 25
W 9/23  3.7  Rotating Unbalance   3.27-32
F 9/25  3.8-10  Equivalent Viscous Damping   3.42,45,54,55
M 9/28    Examples
W 9/30    EXAM 1.  Time: 6:30-7:45 pm,  Location:  106 Sackett
F 10/2  notes  Assign Lab Project
M 10/5  1.11  Fourier Series    1.62-65,67-70
W 10/7   4.1-3  Fourier Series    4.1-4,6,8
F 10/9     Examples
M 10/12 4.4  Convolution Integral   4.12,13
W 10/14 4.5  Convolution Integral   4.17-21,22,23
F 10/16   Examples
M 10/19 4.7  Laplace Transforms   4.46-47
W 10/21   Examples
F 10/23   Assign  Computer Project
M 10/26 5.1-2  Multiple Degree of Freedom Sustems
W 10/28 5.3  Free Vibration of MDOF’s1  5.1,3
F 10/30 notes  Matrix Review
M 11/2  5.3  The Eigenvalue Problem   5.5-7
W 11/4  5.4   Torsional Systems.   5.19,20
F 11/6  notes  Free Vibration of Damped MDOF’s
M 11/9  5.6  Forced Vibration of Undamped MDOF’s 5.24,25-27,30,31
W 11/11    Examples
F 11/13   Examples
M 11/16   EXAM 2. Time: 6:30-7:45 pm,  Location:  327 Sackett
W 11/18 10.3  Vibration Measuring Instruments  10.2,5,11-14
F 11/20 9.10  Vibration Absorbers   9.43,44,52,53
M 11/23 9.6-9  Vibration Control Strategies
W 11/25   no class
F 11/27   no class
M 11/30 8.1-8.2  Continuous Systems, Wave Equation 8.2,6
W  12/2  8.3-4  Vibrating Strings    8.19,21
F 12/4  8.5  Transverse Vibration of Beams  8.33-34
M 12/7    Review
W 12/9    Review
F 12/11   Review

W 12/16 FINAL EXAM. Time: 10:10am, Location 165 Willard

Homework 1
Homework 2
Homework 3
Homework 4
Homework 5:  Problem 3.52 in textbook
Homework 6
Homework 7
Homework 8

Lab 1
Computer Project
Lab 2

Single degree of freedom sytems
Matrix Review 1, 2, 3