ME 370 - Vibrations of Mechanical Systems
Spring 2011, Sec 1 MWF 10:10-11:00am, 135 Reber

Instructor:            Professor Pan Michaleris
                              232 Reber Bldg
                              863-7273
                              pxm32@psu.edu
                              Office hours: Monday 1:20-2:00pm, Wednesday: 11:05-12:00noon

Teaching Assistant: YUE LI, yol5214@psu.edu, 337 Reber, Office Hours: T 9:30-11:00, R1:00-2:30pm.

Text:               Mechanical Vibrations by S.S Rao, 5th Edition.

References on Matlab:

Amos Gilat.  Matlab. An introduction with applications.  John Wiley.  2004.  ISBN: 0-471-43997-5.

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 212 and CMPSC 201 or CMPSC202



Grading Policy , Class Objectives , Course Conduct , Tentative Schedule , Homework , Projects , Notes



Grading Policy:

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



Class Objectives:

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



Course Conduct: Academic Integrity Policy (University Policy 49-20 )

Tentative schedule

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,                                                        Suggested Problems
M       1/10        1.1-6              Introduction, Concepts                          
W       1/12      1.7-10              Elements of Vibratory Systems                   1.1,2,4,5,12,13
F        1/14      2.1-2                Equations of Motion, Newton’s Laws         1.19,24,25,28,29
W       1/19       notes               Energy Methods
F        1/21       notes                Differential Equations Review
M       1/24      2.3-4                Free Vibration of Undamped SDOF’s         2.1,4,5,6,8, 2.11,12,13-16,19,24,27,28
W       1/26      2.6-7                 Free Vibration of Damped SDOF’s             2.49,52,55,60,62,79-84,97
F        1/28     3.1-3                  Forced Vibration of Undamped SDOF’s     3.1,2,6
M        1/31     3.4-5                 Forced Vibration of Damped SDOF’s        3.7,8-11,15-18
W        2/2      3.6                     Base Excitation                                           3.21,22,24, 25
F         2/4        3.7                    Rotating Unbalance                                    3.27-32
M        2/7        3.8-10              Equivalent Viscous Damping  
W       2/9                                 Examples
F        2/11      notes                  Assign Computer Project   
M       2/14                                Examples
W       2/16     1.11                    Fourier Series  
F         2/18    4.1-3                   Fourier Series   
M        2/21    notes                   Convolution Integral
W        2/23    4.4                      Convolution Integral
F         2/25    4.5                       Laplace Transform
M        2/28                                Examples
W        3/2    4.7                        Midterm1: 6:30-7:45pm 114 EES
F         3/4                                 Examples
M        3/7                                 Spring Break
W        3/9                                Spring Break
F         3/11                               Spring Break
M        3/14                              Assign  Computer Project 1
W       3/16        5.1-2               Multiple Degree of Freedom Sustems
F         3/18        5.3                  Free Vibration of MDOF’s1 
M        3/21       notes                Matrix Review
W        3/23       5.3                   The Eigenvalue Problem  
F          3/25       5.4                   Torsional Systems.  
M         3/28                               Examples
W        3/30                               Examples
F         4/1                                  Matlab overview
M        4/4                                 Matlab examples 1
W        4/ 6               Midterm 2: 0630P 0745P   111 Wartik
F          4/8                                Review of Midterm 2
M        4/11                              Assignement of Project 1
W       4/13                               Convolution Integral
F        4/15                                Convolution Integral
M       4/18       8.1-8.2             Continuous Systems, Wave Equation 
W      4/20       8.3-4                 Vibrating Strings   
F        4/22       8.5                    Transverse Vibration of Beams 
M       4/25                                Review
W      4/27                                 Review
F        4/29                                Review



Homework

HW1, Due Jan 28, solution
HW2, Due Feb 4, solution
HW3, Due Feb 11, solution
HW4, Due Feb 18, solution
HW5, Due Feb 25, solution
HW6, Due March 23, solution
Midterm 1 solution
HW7, Due April 1, solution
HW8, Due April 15, solution
Computer project, Due April 22
Midterm 2 solution


Projects
  



Notes

ODE Review

dof1.m
Problem solutions: Ch1, ch1, ch2, Ch2, Ch3, ch3, ch4, ch5, ch8
SDOF summary

Fourier
Free2DOF
Free2dofmatlab

2dfree
2dforced

2dof free with damping
2dof foced with dampling dofcp1
vibraiton absorber with damping