Instructor:            Professor Pan Michaleris
                              232 Reber Bldg
                              863-7273
                              pxm32@psu.edu
                              Office hours: Monday & Wednesday: 2:30-3:25 pm

Teaching Assistants:  Section 1: HAFTAY HAILU <huh109@psu.edu> 220 Reber, T, Tr 3:00-4:30 pm
                                     Section 2: LU ZHANG <lxz133@psu.edu> 241 Reber, Desk13, Tr 3:00-5:00pm

Text:               Mechanical Vibrations by S.S Rao, 2nd and 3rd Edition.

References on Matlab:

D. M. Etter, D. C. Kuncicky, D. Hull. Introduction to MATLAB 6, Prentice Hall 2001. ISBN:0-13-032845-5.

D. Hanselman, B. Littlefield. Mastering MATLAB 6, A comprehensive tutorial and reference, Prentice Hall 2001. ISBN:0-13-019468-9.

E. B.Magrab, S. Azarm, B. Balachandran, J. Duncan, K. Herold, G. Walsh. An engineer's guide to MATLAB,
Prentice Hall 2000. ISBN : 0-13-011335-2.

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

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

Upon completion of this course, students should be able to:

1) Use Newton's Second Law and free body diagram approach to model vibratory systems
2) Solve differential equations and eigenvalue problems for determining the dynamic response (with correct units) of vibratory systems
3) Understand the physical and mathematical significance of:
        natural frequencies and mode shapes
        free and forced response
        resonance
        damping
        superposition
        lumped parameter vs continuous systems
        linear vs non-linear systems
4) Use appropriate analytical, numerical and computational tools
5) Understand experimental and data analysis techniques
6) Design mechanical systems with prescribed vibratory performance

• Class attendance is highly recommended as material is frequently presented which departs from the text.
• Homework problems will be assigned approximately once a week and will be due one week later.
• There will be two mid-term examinations.
• We will assign one lab and two computer projects. 
• 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 four pages of notes.

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
M     1/13        1.1-6       Introduction, Concepts
W     1/15      1.7-10      Elements of Vibratory Systems  1.1,2,4,5,12,13
F       1/17      2.1-2        Equations of Motion, Newton’s Laws 1.19,24,25,28,29
M      1/20      notes        Energy Methods
W     1/22       notes        Differential Equations Review
F       1/24      2.3-4        Free Vibration of Undamped SDOF’s 2.1,4,5,6,8
M      1/27      2.5           Free Vibration of Undamped SDOF’s 2.11,12,13-16,19,24,27,28
W      1/29      2.6-7       Free Vibration of Damped SDOF’s  2.49,52,55,60,62,79-84,97
F        1/31     3.1-3        Forced Vibration of Undamped SDOF’s 3.1,2,6
M       2/3     3.4-5        Forced Vibration of Damped SDOF’s 3.7,8-11,15-18
W      2/5      3.6           Base Excitation    3.21,22,24, 25
F        2/7        3.7           Rotating Unbalance   3.27-32
M       2/10        3.8-10     Equivalent Viscous Damping   3.42,45,54,55
W       2/12                       Examples
F        2/14      notes       Assign Lab Project   
M       2/17     EXAM 1   6:30-7:45  pm  22 Deike
W       2/19     1.11         Fourier Series    1.62-65,67-70
F         2/21    4.1-3        Fourier Series    4.1-4,6,8
M        2/24    notes        Examples
W        2/26    4.4           Convolution Integral   4.12,13
F         2/28    4.5            Convolution Integral   4.17-21,22,23
M        3/3                     Examples
W        3/5    4.7            Laplace Transforms   4.46-47
F         3/7                       Examples
M        3/10                      Spring Break
W        3/12                       Spring Break
F         3/14                       Spring Break
M        3/17                     Assign  Computer Project 1
W       3/19        5.1-2     Multiple Degree of Freedom Sustems
F         3/21        5.3        Free Vibration of MDOF’s1  5.1,3
M        3/24       notes     Matrix Review
W        3/26       5.3         The Eigenvalue Problem   5.5-7
F          3/28       5.4         Torsional Systems.   5.19,20
M         3/31                     Examples
W        4/2                      Examples
F         4/4                     Free Vibration of Damped MDOF’s
M        4/7          notes  Assign  Computer Project 2    
W        4/9                        Midterm 2: 6:00-7:30pm 362 Willard
F          4/11        5.6          Forced Vibration of Undamped MDOF’s 5.24,25-27,30,31
M        4/14        10.3         Vibration Measuring Instruments  10.2,5,11-14
W       4/16       9.10         Vibration Absorbers   9.43,44,52,53
F        4/18       9.6-9       Vibration Control Strategies
M       4/21       8.1-8.2     Continuous Systems, Wave Equation 8.2,6
W      4/23       8.3-4        Vibrating Strings    8.19,21
F        4/25       8.5           Transverse Vibration of Beams  8.33-34
M       4/28                        Review
W      4/30                        Review
F        5/2                        Review

ODE Review (p1 , p2 , p3 , p4 , p5 , p6 , p7 )

Midterm1 sample , solution p1 , p2  
Midterm2 sample , solution p1 , p2 ,  p3 , p4
Final samlpe, p1 , p2 , p3 , p4 , p5 , p6 , p7 , p8

Single degree of freedom sytems
Matrix Review 1 , 2 , 3
Matlab sample files: Fourier series