Welcome to the course home page for ME/EMA 540. Use the links below to find the lecture slides, homework assignments, solutions, lab handouts, etc... The following sections outline the preparation that you must do for each class period (i.e. reading and assignments), the learning outcomes, and the homework.

Instructor: Prof. Matt Allen, msallen@engr.wisc.edu, Google Voice Phone: (262) 235-3265, 525 ERB, Office Hours: Tues 2:30-3:30PM, Wed 11-12PM, or by appointment, Meet on BBCollaborate Ultra Page: (Tuesdays) https://us.bbcollab.com/guest/e562212b3042457fb5896d05d53b7192 (Wednesdays) https://us.bbcollab.com/guest/f2a8214f907b4821b56a3620a8a72f87,
Other times in WebEx meeting room: https://uwmadison.webex.com/meet/pr929592798

Teaching Assistant: Benjamin Moldenhauer, bmoldenhauer@wisc.edu, available by appt. online on a limited basis. Please use Prof. Allen's office hours or Piazza as a first recourse.

Course Email List: ema540-1-f20@g-groups.wisc.edu

Meeting Time: MW 2:30-3:45PM ONLINE or in 2163 ME as noted in the schedule below. Labs may include time outside of these hours.

### Official Syllabus ###

Anonymous feedback form: https://forms.gle/uSpN7PqCTiPb5Jfo7

Course Materials:
Textbook errata, etc... (Ginsberg)
Lecture Notes (PDF)
Matlab Scripts
Homework Assignment Files
Homework Solutions

Key to abbreviations below. On days noted we will meet in the Lab, room 2163 ME.
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, HW = homework problems relevant to the lecture

Eight Things Engineering Students Should Know About Blended Learning

Other Resources:

Experimental Techniques - Articles on Modal Analysis (single PDF file containing all articles)

Date*	Topic	Due Dates*
9/2	Introduction, 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 Video, 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 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
9/7	Labor Day Holiday	HW #2 Assigned
9/9	MDOF Systems: Free Response / Generalized EVP LO: Understand eigenvalue problem and able to find modes from M & K in Matlab. Introduce Lab #1 Lec: Video, Notes 1, Notes 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)*
9/14	Lab 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 Handout Lab 1 Handout - Free vibration of SDOF/MDOF Systems You 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: 4:00-5:30 The 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
9/16	LO: 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 ICEx: HW#3	*HW#2 due* *HW#3 due (Friday evening)*
9/21	Forced 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=3e^i0.8, c.) A=1/(1-2i), d.) A=1/(3e^i0.8). Lec: Review SDOF Force Response, Video, Notes ICEx: HW#4 Prob. 1-2	HW #4 Assigned
9/23	Read: 5.0-5.2 (p. 294-299). Skim: Example 5.2 Lec: Review MDOF Frequency Domain FRF, Modal Representation, Video, Notes	*L1 Report Due*
9/28	Lab 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*
9/30	Final 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 PCA: Overview of Test Plan, Slides	*Choose Project Teams Due*
10/5	Fourier Series, DFT, Sampling PCA: Watch the FFT_Introduction video Read: Handout, 3.7.1 - 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
10/7	Fourier Series Analysis and FFT Lec: Square Wave Example Problem with FFT ICEx: Q&A for HW#5
10/12	Lec: Leakage, Aliasing & FFT For Transient Response ICEx: Q&A for HW#5 - Bring your questions!
10/14	(two lecture videos for today) Lec: 1.) FRF Estimation, Notes, HW#6P2, 2.) Finish Experimental Modal Analysis (SIMO, MISO, MIMO), Notes HW#6P1 Optional Reading: Avitabile Modal Analysis Overview	*HW #5 Due,* HW #6 Assigned
10/19	Lec: (Video, Slides): Modal Parameter Estimation, HW#6P3 Read: 5.3 Vibration Absorber Lec: Vibration Absorber (Repeat of EMA 545)	*L2 Report Due*
10/21	Mid-Term Exam on Concepts from HW1-HW5, Practice Exam, Rough solution
10/26	Lec: Operational Modal Analysis (Video, Slides, Notes) You can now begin analysis of the measurements taken for the final project.
10/28	Lec: Sensors: Accelerometer, Vibrometer, Strain gauge, etc… , (Video, Slides) HW#7	**HW #7 Assigned, HW #6 Due**
11/2	Read: 6.1.1 (p. 326-335) Lec: Intro to Continuous Systems / Ritz, (Video Part 1, Mod 3 Slides, Video 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
11/4	Introduce Lab #3, Work on HW#7 in class	*HW #7 Due (Friday)* HW #8 (Lab 3 Analysis) Assigned
11/9	Lab 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
11/11	Lab 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*
11/16	Lec: Support Conditions (Video, Mod 3 Slides)
11/18	Lec: MAC, MSF, Video on BBCollab, Notes ICEx: Work on Lab 3 Reports	*HW #9 Due*
11/23	Lec: Finite Element Models, Video, (Slides in Module 04 Ritz-FEA), ICEx: Work on Lab 3 Reports
11/25	ICEx: Work on Lab 3 Reports Thanksgiving Recess 11/26 – 11/29	*L3 Report Due*
11/30	Open for teams to work on their final projects, Final Project Assignment Posted
12/2	Lec: 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*
12/7	Open for teams to work on their final projects
12/9	Open for teams to work on their final projects
12/16	Final Reports Due Final Exam Period, 12/16/2019, Wednesday, 2:45PM-4:45PM	Final Reports Due