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
Homework Solutions
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 (Links to an external site.), SDOF Free Response Part 2 Video (Links to an external site.)Notes, 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 downloadSome Articles from Sound and Vibration MagazineHow 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 downloadRevised Example 2.5 downloadAdditional videos in case they are helpful for review:Video Lecture Numerical Integration (Links to an external site.)Video Part 2 EOM with Coulomb Friction (Links to an external site.)
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 (Links to an external site.)Notes 1Notes 2, HW2P3-6
Read: 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 (Links to an external site.) 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 (Links to an external site.)Notes
ICEx: 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, Video (Links to an external site.)Notes
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, Video (Links to an external site.)Notes
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 (Links to an external site.) (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 Plan (Links to an external site.)Slides
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
Lec: Square Wave Example Problem with FFT (Links to an external site.)
ICEx: Q&A for HW#5
10/12Lec: Leakage, Aliasing & FFT For Transient Response (Links to an external site.)
ICEx: Q&A for HW#5 – Bring your questions!
10/14(two lecture videos for today)
Lec: 1.) FRF Estimation (Links to an external site.)Notes, HW#6P2, 2.) Finish Experimental Modal Analysis (Links to an external site.) (SIMO, MISO, MIMO), Notes HW#6P1
Optional ReadingAvitabile Modal Analysis Overview
HW #5 Due, HW #6 Assigned
10/19Lec: (Video (Links to an external site.)Slides): Modal Parameter Estimation, HW#6P3
Read: 5.3 Vibration Absorber
Vibration Absorber (Repeat of EMA 545) (Links to an external site.)
L2 Report Due
10/21Mid-Term Exam on Concepts from HW1-HW5, Practice ExamRough solution 
10/26Lec: Operational Modal Analysis (Video (Links to an external site.)SlidesNotes) You can now begin analysis of the measurements taken for the final project. 
10/28Lec: Sensors: Accelerometer, Vibrometer, Strain gauge, etc… , (Video (Links to an external site.)Slides) HW#7HW #7 Assigned, HW #6 Due
11/2Read: 6.1.1 (p. 326-335)
Intro to Continuous Systems / Ritz, (Video Part 1 (Links to an external site.)Mod 3 SlidesVideo Part 2 – Matlab Example (Links to an external site.))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 (Links to an external site.)
Hammer Modal Test of Hard Drive Using B&K Pulse-Part 2  (Links to an external site.)
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 (Video (Links to an external site.)Mod 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 (Links to an external site.), (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 (Links to an external site.), 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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