Fundamental of Vibration
ME:4153
Spring 2025
http://icon.uiowa.edu
Instructor
Jia Lu, Professor of Mechanical Engineering
Phone: 335-6405; E-mail: jialu@engineering.uiowa.edu
Zoom Office Hours: T Th 1:00pm-2:00pm, or by appointment
Lectures:
T Th 5:00am – 6:15pm, 4030SC
Catalog Data
ME:4153: Fundamental of Vibration. 3 Credits. The same as CEE:4533
Analysis and evaluation of the vibration of linear discrete and continuous systems.
Modeling techniques and simulations for vibration response, various excitations, model
analysis, and engineering applications.
Prerequisite:
ENGR:2750 Mechanics of Deformable Bodies
Textbook: Dan J. Inman, “Engineering Vibration”, 4th edition, Pearson, 2014. Available
via ICON Direct
Reference: Lecture Notes
Grading:
* Homework ............................................
* Project 1 .….……...............................
* Project 2 ………….............................
* Project 3 …….....................................
* Midterm Exam ...................................
55 %
10 %
10 %
10 %
15 %
Course Objective: Develop an understanding of the fundamentals of vibration. Acquire
the ability to solve vibration problems, and analyze vibration system.
Course topics
• Single DOF system: Undamped free vibration; damped free vibration; harmonic
loads; general loads and Duhamel’s integral; energy methods for deriving
vibration equations.
• Vibration design: Transmissibility functions; vibration reduction; vibration
design; response spectra.
• Multiple DOF systems: Modal analysis; method of mode superposition. Timefrequency signals; frequency domain solution (if time permits);
• Continuum systems: Vibration of elastic strings and bars; torsional vibration of
shaft; finite element method for structural vibrations (if time permits).
Scheduling conflicts
Students anticipating a scheduling conflict should contact the instructor as soon as
possible. Exams could be arranged at alternative times as consistent with the University’s
exam policies.
Collaboration Policy
Discussion of homework and lab problems with other students is encouraged. This is a
good way to learn from each other and develop teamwork skills. However, direct copying
of any assignment, in part or whole, is strictly prohibited. College regulations recommend
that a zero be given in all assignments if this policy is violated.
Lecture Schedule
Week Date
1
2
3
4
5
6
7
8
9
11
12
13
14
15
16
1/21
1/23
1/28
1/30
2/4
2/6
2/11
2/13
2/18
2/20
2/25
2/27
3/4
3/6
3/11
3/13
3/25
3/27
4/1
4/3
4/8
4/10
4/15
4/17
4/22
4/24
4/29
5/1
Topics
Introduction. Spring mass system
Harmonic motion
Damping
Energy method
Stiffness measurement
Design considerations
Harmonic excitation, beats
Harmonic excitation, resonance
Harmonic excitation, damped system
Base vibration. Project I kickoff
Rotation unbalance. Vibration reduction.2.4-2.6
Response to general forces
Shock spectrum
Periodical force. Fourier series
Transformation method. Random vibration
Midterm Exam
Spring Break
Undamped two DOF system. Project II kickoff
Modal analysis
More than two DOF systems
Forced response of more than two DOF systems
Systems with viscous damping. Lagrangian equation
Vibration suppression
Critical speed of rotating shaft
Vibration of strings and cable
Longitudinal vibration of bars. Torsional vibration
Modal superposition of continuum system
Finite element method for vibration
Finite element (contd.), Project III
Text
1.1
1.1-1.2
1.3
1.4
1.5-1.6
1.7
2.1
2.2
2.2
2.4
3.1-3.2
3.6
3.3
3.4, 3
4.1
4.3
4.4
4.6
4.5,4.7
5.1-5.3
5.7
6.1
6.3,6.4
6.8
8.1-8.3