EMA 545: Mechanical Vibrations

Official Syllabus – Abbreviated/Formatted Syllabus

Abbrevations Key:
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



Due Dates
1/22 Lec: Introduction, Syllabus, etc…
LO: How is this class used in engineering practice?
1/24 Lec: Review of Newton-Euler EOM
Read/Review: 1.1-1.4
LO: How do I find the equations of motion for a spring-mass-damper system? How do these elements relate to real engineering structures?
1/27 PCA: HW#1, Probs 1-3 (deleted)

Read: 2.0-2.1.1
Lec: Numerical solution methods, Solutions to EOM, Harmonic Functions
LO: Learn to derive solutions for SDOF free response.

1/29 LO: Learn to manipulate complex exponential descriptions of vibration.
Read: 2.1.2 (revised online), 2.1.3 (Beating) to p. 70, Ex. 2.3, 2.4, 2.5 (revised online)
1/31 Lec: Nondimensionalizing EOM and Frequency Scaling
ICEx: HW#2, Probs 2-4
HW #1 due
2/3 Lec: Free Response: Underdamped/Overdamped (2.2)
2/5 Read: 2.2.3 Overdamped, Skim: 2.2.4 Critically Damped
Lec: Forced Response (2.3.0-2.3.4, Skip 2.3.5), Forced Response Example, RF Switch Example
2/7 Lec: RF Switch Example (Forced Transient Response). Golf club shaft example. HW #2 due
2/10 LO: Improve Matlab skills and to solve transient forced response problems in Matlab.
PCA: HW#3 Prob. 1,5b (not graded), ICEx: HW#3, Probs 4,5a,c
2/12 (continued)
2/14 Read: 3.2.1, Skim: 3.2.2, 3.3 Resonance
Lec: Aircraft Engine Example, Start Frequency Response
HW #3 due
2/17 Lec: Frequency Response (3.0-p. 126)
2/19 PCA: Read Handout. Find EOM for HW#4, Prob. 6 and turn in before the end of class.

ICEx: Work on HW#4

2/21 Lec: Rotating Imbalance (3.4), Base Excitation (Ex. 3.2), Force Transmission (3.6) Half Power Points (3.2.1), Structural damping (3.2.2) HW #4 due
2/24 LO: How do we determine whether vibration will cause an element to break?

Lec: Stress in Springs (notes)

2/26 Read: Watch FFT Introduction Video, Ginsberg: 3.7.1 – 3.7.3, Ex. 3.9, 3.7.5. Skim: 3.7.4, 3.7.6
Read: Summary of Fourier Series / FFT AnalysisICEx: Work on HW5 Prob. 3-5
2/28 Lec: Fourier Series (3.7), Response of SDOF System to a Square Wave Force with FFT (lecture notes at this link) HW#5 due
3/2 Lec: FFT for Transient Excitation (3.8.2), Accelerometer (3.7.6)
3/4 Lec: Aliasing, Leakage, FFT to Analyze Music & Noise, ICEx: Work on HW#6 HW#6 due
3/6 ICEx: Q&A on practice exams
3/9 Exam #1 (Ch. 2-3, SDOF Response, through HW#4)
3/11 Lec: MDOF EOM, Large Deformation & Linearization (1.5)
3/13 Lec: MDOF Nonlinear EOM continued
3/16-3/20 Spring Recess (Mar 16-20)
3/23 PCA/Read: Video on Kaltura Links to an external site.(watch prior to class!) Handout: Mod04a…
Lec: Finish Lagrange NL EOM, Gravity Stiffness
3/25 Read: 1.5.4:Potential Energy (p.34-41), Stiff Spring Approx, Examples (1.5.3)
Lec: Power Balance Examples, Physical Checks on the EOM, Notes Mod04c...
Video/Handout: Shuttle Example (Links to an external site.)
ICEx: HW7 Prob. 3(c), Prob. 5
HW #7 due
3/27 Video Lec: Power Balance Examples (Links to an external site.) (Kaltura), Physical Checks on the EOM, Handout 1, Handout 2 HW #A1
3/30 Lec (Live / Video on BBUltra (Links to an external site.)): MDOF Solution – Intro to Eigenvalue problem (4.1), Solving Eigenvalue Problems in Matlab
4/1 No Video. Read: Examples 4.1 and 4.4 (p. 238-239 only). Review: sec. 4.2.1 if these examples are not clear.

PCA: HW8 Prob 3 (turn in online), ICEx: HW8 Prob. 4

4/3 Read: 4.2.2 Orthogonality & Normalization, Skim 4.2.3 and 4.2.4
Video Lec: Orthogonality, Normalization & Examples (Links to an external site.), Handout
ICEx: Work on HW#8
HW #8 due
4/6 Video Lec: Modal Analysis with Damping, Application to Earthquakes (Links to an external site.), Handout
ICEx: Work on HW#9, Lec (Video BBColab): Solve Prac Ex2aP3
4/8 Video Lec: Modal Transformation for Forced Response (Links to an external site.), Handout
Lec (Video BBColab): Solve Prac Ex2aP2
4/10 Review Exam #1 (Video BBColab) HW #9 due
4/13 Video Lec/PCAClose Natural Frequencies, 3DOF Example (Links to an external site.) (PCA/Handout )
Lec: Review Prac. Exams: Checking EOM (notes now posted)
4/15 Review for Exam #2
4/17 Video Lec: Steady-State Response with Modal Analysis (Links to an external site.), Notes
4/20 Exam #2 – MDOF EOM and basics of EVP, 9:30AM-11AM
4/22 Video Lec: MDOF Frequency Domain Transfer Function (Links to an external site.) (Ch. 5)
4/24 Work on Final Projects
4/27 Video Lec: Vibration Absorber (Links to an external site.) (Ginsberg 5.3)
Work on Final Projects
HW#10 due
4/29 Lec: Coordinate Transformations, Lec: Application Example: Cell phone drop
End of Course Evaluations: https://aefis.wisc.eduLinks to an external site.
Work on Final Projects
5/1 Work on Final Projects HW #11 (canceled)
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