EMA 540: Experimental Vibration and Dynamic System Analysis

Official Syllabus

Course Materials:
Textbook errata, etc… (Ginsberg), Link to Book at UW-Library (Links to an external site.)
Lecture Notes (PDF)

Matlab Scripts
Homework Assignment Files
Video Lectures (Youtube) (Links to an external site.)

Key to abbreviations below:
LO = Learning Outcome
Read = Mandatory Reading
Review/Skim = Optional reading
PCA = Pre-Class Assignment.  These are due at the beginning of the following class and will be graded as homework problems.
ICEx = In Class Exercise
Lec = Lecture, Relevant HW Problems (green)

Activities/due dates/etc shown with orange text are subject to change

Date*TopicDue Dates*
9/2Introduction, SDOF Free Response
LO: How is this class used in engineering practice? Understand the form of SDOF free response and be able to manipulate it to solve problems. Understand response of damped SDOF system.
Lec: Introduction Part 1 Video, SDOF Free Response Part 2 VideoNotes, HW1, HW2P1-2
Read: 2.1.2 (see below), 2.1.3 to p. 70, Ex. 2.3, 2.4, 2.5 (see below), 2.2.2-p.79-83, Review: 2.1.1-p.71-73, 2.2.0-2.2.1, p. 84-90
ICEx: HW#1, Probs 1-3(Sorry to give you so much on the first day, but this will ease our schedule later.)
Additional Resources
Vibration Measurement from Lexus GS 300
Some Articles from Sound and Vibration Magazine
How to search S&V Magazine: The search feature on sandv.com doesn’t currently work very well. Instead, in Google type: “sandv.com aircraft ground vibration test” (without quotes, replace the keywords with whatever you’re interested in).  Ginsberg Chapter 2, Sec. 1-2.2.2 Corrected,
Revised Example 2.5
Additional videos in case they are helpful for review:
Video Lecture Numerical Integration
Video Part 2 EOM with Coulomb Friction 
HW#1 Assigned
9/7Labor Day HolidayHW #2 Assigned
9/9 MDOF Systems: Free Response / Generalized EVP
Understand eigenvalue problem and able to find modes from M & K in Matlab. Introduce Lab #1
LecVideo, Notes 1Notes 2, HW2P3-6
4.2 – 4.2.1 and Ex. 4.4, Review: 4.1, 4.2.5, 4.2.6, Ex. 4.1
HW#1 due (Friday)
9/14Lab 1:  SDOF/MDOF Transient Response (CHANGED TO VIRTUAL on BBCollab)
LO: Observe the theory regarding SDOF/MDOF free response illustrated on a simple experiment. Critically evaluate how well the theoretical model fits measurements.
PCA: Read Lab #1 HandoutLab 1 Handout – Free vibration of SDOF/MDOF SystemsYou will do the lab in groups of 2-3.  You have been randomly assigned to a group in Canvas, which should show up in the lab assignment and on the “People” section of the course homepage. Teams 2 and 4: 2:30-3:30, Teams 1 and 3: 4:00-5:30The live demo was recorded on BBCollaborate Ultra (click on the hamburger on the top left, then “Recordings”).  Also, this video shows a demo that Allen recorded this past summer. 
HW #3 Assigned
9/16LO: Where does damping come from? How do we find the damping ratios for a system after uncoupling the EOM using the modes?
Read: 4.2.2 (P.230-235), 4.3.1-2, 4.3.4, Ex. 4.8 Review: 4.2.5-6. Skim: 4.2.3-4, 4.3.3
Lec: Video,  Notes
: HW#3
HW#2 dueHW#3 due (Friday evening)
9/21Forced Steady-State Response, SDOF/MDOF
Read: 3.1 through Ex. 3.2 and 3.2.1-2. Skim: 3.2.0, 3.3-3.6. 
PCA: Sketch A in the complex plane for the following cases: a.) A=1-2i, b.) A=3ei0.8c.) A=1/(1-2i), d.) A=1/(3ei0.8).
Lec: Review SDOF Force Response, VideoNotes
ICEx: HW#4 Prob. 1-2
HW #4 Assigned
9/23Read: 5.0-5.2 (p. 294-299). Skim: Example 5.2
Lec: Review MDOF Frequency Domain FRF, Modal Representation, VideoNotes
L1 Report Due
9/28Lab 2: Frequency Response of SDOF/MDOF Sys. (2163 ME)
2:30-3:45: Teams 1 and 2
4:15-5:30: Teams 3 and 4
LoadUFF Demo (see Matlab folder for files)  
HW #4 Due
9/30Final Project Testing (Meet at 2nd floor walkway between ERB and Materials Science)
Each team should come in shifts to help with the testing. You are welcome to stay longer if you are able.
2:30-3:30 – Team 1, 3:30-4:30 – Team 2, 4:30-5:30 – Team 3
PCAOverview of Test PlanSlides
Choose Project Teams Due
10/5Fourier Series, DFT, Sampling
PCA: Watch the FFT_Introduction video
Read: Handout3.7.1 – 3.7.3, Ex. 3.9, 3.7.5. Skim: 3.7.4, 3.7.6
Matlab Examples: FFT_Square_Ex_540_v4.m, FFT_LeakageExample.m
HW# 5 Assigned
10/7Fourier Series Analysis and FFT
 Square Wave Example Problem with FFT 
ICEx: Q&A for HW#5
10/12Lec: Leakage, Aliasing & FFT For Transient Response 
Q&A for HW#5 – Bring your questions!
10/14(two lecture videos for today)
Lec: 1.) FRF EstimationNotes, HW#6P2, 2.) Finish Experimental Modal Analysis (SIMO, MISO, MIMO), Notes HW#6P1
Optional ReadingAvitabile Modal Analysis Overview
HW #5 Due, HW #6 Assigned
10/19Lec: (VideoSlides): Modal Parameter Estimation, HW#6P3
Read: 5.3 Vibration Absorber
Vibration Absorber (Repeat of EMA 545) 
L2 Report Due
10/21Mid-Term Exam on Concepts from HW1-HW5, Practice ExamRough solution 
10/26Lec: Operational Modal Analysis (VideoSlidesNotes) You can now begin analysis of the measurements taken for the final project. 
10/28Lec: Sensors: Accelerometer, Vibrometer, Strain gauge, etc… , (VideoSlides) HW#7HW #7 Assigned, HW #6 Due
11/2Read: 6.1.1 (p. 326-335)
Intro to Continuous Systems / Ritz, (Video Part 1Mod 3 SlidesVideo Part 2 – Matlab Example)Read: 6.1.3 (p. 341-350)
Lec: Ritz Method for Beams (6.1.3-4, 6.2), Live lecture on BB Collaborate
11/4Introduce Lab #3, Work on HW#7 in class HW #7 Due (Friday)HW #8 (Lab 3 Analysis) Assigned
11/9Lab 3: Impact Modal Test of F-F Beam (2163 ME)
PCA (turn in as HW#8a)
: 1.) Read lab handout
2.) Watch video below on use of B&K software
Hammer Modal Test of Hard Drive Using B&K Pulse-Part 1 
Hammer Modal Test of Hard Drive Using B&K Pulse-Part 2  
3.) Use Appendix C to calculate the first 3 nonzero (elastic) natural frequencies of the beam that your team was assigned.  This will let you know what frequency range you expect to have to test in the lab. Upload your answer online.
Team 1 – Beam 2
Team 2 – Beam 6
Team 3 – Beam 7
HW #8a Due
11/11Lab 3: Continued
PCA (turn in as HW#8b): Perform preliminary modal analysis on your measurements, to check the quality of the fit and your frequency spacing. 
HW #8b Due
11/16Lec: Support Conditions (VideoMod 3 Slides) 
11/18Lec: MAC, MSF, Video on BBCollab, Notes
ICEx: Work on Lab 3 Reports
HW #9 Due
11/23Lec: Finite Element Models, Video, (Slides in Module 04 Ritz-FEA), ICEx: Work on Lab 3 Reports
11/25ICEx: Work on Lab 3 Reports
Thanksgiving Recess 11/26 – 11/29
L3 Report Due
11/30Open for teams to work on their final projects, Final Project Assignment Posted 
12/2Lec: Nonlinear Vibration, Video, See also Module 7 Slides on Canvas
Example of how to calculate auto- and cross-spectra in Matlab & BBCollab Recording
HW #10 Due
12/7Open for teams to work on their final projects
12/9Open for teams to work on their final projects 
12/16Final Reports Due
Final Exam Period,  12/16/2019, Wednesday, 2:45PM-4:45PM
Final Reports Due

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