Post on 24-Feb-2018
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Mechanical Vibrations
(MECE 3210)
Instructor: Dr. Amirhossein Monjazeb, P. Eng.
With special Thanks to Professor Fred Afagh for providing me with hisinvaluable lecture notes and for his full support
Winter 2016
Lecture # 01
Some contents, figures, and problems of the presented slides are completely adopted or partially revised from:Mechanical Vibrations, Fifth Edition, S.S. Rao, Prentice Hall, 2011, ISBN: 978-0-13-212819-3.
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A Brief History of Vibrations
MECE 3210 Mechanical Vibrations Lecture # 01 2
Musical instruments and vocal vibrations
Pythagoras (582-507 B.C.) - Monochord
Aristotle (350 B.C.) - Multichord
Zhang Heng (Second Century) - First earthquake measurement device
Galileo Galilei (1564-1642) - Studied the behavior of a simple pendulum
Pythagoras
Galilei
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Monochord
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Pendulum Vibration Process
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mg
21
3
1:
Potential Energy Kinetic Energy
Mass (m)
= (1 cos )
= 0 K. E. = 0
2:
P. E. = . (1 )
Starts swinging to the right Angular Acceleration
Potential Energy
Conversion
ConvertedKinetic Energy
Mass m will continue moving towards point 3
Again, gravity torque causes a C.C.W. velocity
3: = 0 Potential EnergyConverted
Kinetic Energy
As it crosses point 2, a C.C.W. torque (due to gravity)starts acting on the mass resulting in deceleration
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Why we need to study mechanical vibrations?
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In many engineering designs, we need toeliminate or control mechanical vibrations
In many engineering designs, we need tocreate vibrations
To create or eliminate vibrations inmechanical systems, we must be able tocreate mathematical models and analyzethe wanted or unwanted vibration.
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Undesired Mechanical Vibrations
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Undesired Mechanical Vibrations
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Desired Mechanical Vibrations
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Terminology
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M
Mass The quantity of matter in a body regardless of its volume or
of any forces acting on it.
(with negligible elasticity and damping)
Stiffness
How freely or easily can a mass move during vibration(a mechanical link with negligible mass and damping)
Damping
Absorbs the energy in a vibrating system(a mechanical link with negligible mass and elasticity)
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Mass-Spring-Damper Model
M
()
()
The amplitude (A) of a vibrating mass (system) defines itsmaximum displacement from its equilibrium position
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Pendulum Vibration Process
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g
2
13
M
Potential Energy Kinetic Energy
External source of energy to maintain a steady state
Dissipated energy (if damper)
Conversion
Mass/Inertia-Means to store Kinetic Energy
Spring/Elasticity-Means to store Potential Energy
Means by which energy is gradually last
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Mass-Spring-Damper Models
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Mass-Spring Model
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m
mg
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m
Mass-Spring Model
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m
Mass-Spring Model
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m
Mass-Spring Model
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m
Mass-Spring Model
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m
Mass-Spring Model
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m ()mg
= sin( + )
Maximum Amplitude
(/)= 2 ()
Phase (rad)
()
= 0
Mass-Spring Model
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()
= 0
2
= 2. =
.
Mass-Spring Model
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()
2
M N
2
L
2
Mass-Spring Model
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()
Mass-Spring Model
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Vibration and Fugue
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Vibration and Fugue
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Fugue-Modeling
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m
()mg
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m
mg
Fugue-Modeling
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m
Fugue-Modeling
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m
Fugue-Modeling
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m
Fugue-Modeling
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m
Fugue-Modeling
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m
Fugue-Modeling
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m
Fugue-Modeling
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m
Fugue-Modeling
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m
()mg
Fugue-Modeling
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m
()mg
Fugue-Modeling
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m
Fugue-Modeling
MN
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Mass Spring Damper Models
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Mass-Spring-Damper Models
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()
2
M N
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Course Objective and Outcomes
Objective
understand the fundamental concepts of mechanical vibration
Outcomes
analyze free vibration of single degree-of-freedom systems analyze vibrating systems excited by a harmonic force
design appropriate vibration isolators
analyze forced vibration of systems under general forcing condition
investigate vibration of systems with two-degree-of-freedom
design appropriate dynamic vibration absorbers analyze systems with many degree-of-freedoms
design dynamic systems having coupled coordinates
use computer tools, such as MATLAB, to design and simulate vibrating systems.
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Prerequisites
ENGR 2020 - STATICS AND DYNAMICS [Min Grade: D]
OR
ENGR 2430 - DYNAMICS [Min Grade: D]
OR
MECE 2430 - DYNAMICS [Min Grade: D]
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Major Topics
Fundamental concepts of vibrations of mechanical systemsfree vibrations of single-degree-of-freedom systems
various types of damping and vibration absorption
forced vibrations; vibration measuring instruments
torsional vibrations of shaftssteady-state and transient vibrations
vibrations of multi-degree of freedom systems
vibration isolation
model analysis
vibrations of coupled systems
introduction to non-linear springs and non-linear damping
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Required Course Text
Mechanical Vibrations, Fifth Edition,
S.S. Rao, Prentice Hall, 2011, ISBN:
013-212819-3.
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Reference Books and Information Sources
Engineering Vibration, Third Ed., Daniel J. Inman, Prentice
Hall, 2008, ISBN: 13-9780132281737
Mechanical Vibration, W.J. Palm III, Wiley, 2007, ISBN: 0-471- 34555-5
Theory of vibration with application, Fifth Edition, W.T.
Thompson and M. D. Dahleh, Prentice Hall, 1998, ISBN: 0-13-651068-X
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How to Contact me
43
My OFFICE HOURS: ENG- 1025
You are always welcome to drop by my office whenever I am there and
I have time
Wednesdays 2:00 PM to 4:00 PM
Contact:Only
Via Blackboard
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TAs Information
44
Name Nadim Arafa Omar Sadek
Email Nadim.Arafa@uoit.ca Omar.Sadek@uoit.ca
Office TBA TBA
Office Hours TBA TBA
There are twelve weekly tutorial problem sets which are placed in the
corresponding bunker.
Students are encouraged to study the course materials before solving the problems.
The lectures posted on Blackboard may not cover all the material.
It is strongly recommended that students attend every class and tutorial sessions
although attendance will not be taken.
MECE 3210 Mechanical Vibrations Lecture # 01
mailto:Nadim.Arafa@uoit.camailto:Omar.Sadek@uoit.camailto:Omar.Sadek@uoit.camailto:Nadim.Arafa@uoit.ca7/25/2019 01 Vibrations Lecture 1
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Final Grade Breakdown
45
Assignments: 10%
Laboratories: 10%
In class Quizzes: 5% (bonus)
Midterms: 30%
Exam: 50%
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Midterm Exam
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Midterm Date:
Friday, March 4, 2016 - 05:10 PM to 06:30 PM
Midterm Location:
Library Portables UL11
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Lab Description
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1.Vibration of spring
mass systems.
2.Free vibration of a singledegreeoffreedom system
3.Free damped vibration
4.Forced damped and undamped vibration
5.Vibration of a twodegreeoffreedom system
Please check your lab schedule on
Blackboard/Contents/Labs
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Computer Experience
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MATLAB will be used in solving problems
throughout the course.
Problems solved by MATLAB must be shown
in full with the steps taken.
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Assignments
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There are five sets of assigned homework placed in the
corresponding bunker.
There are few problems solved in class, which are related to thetopics covered in the lectures. However, during the semester
additional practice problems will be given to the students to get
prepared for their mid-term and final exams.
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Assignments
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There are five sets of assigned homework placed in the
corresponding bunker.
There are few problems solved in class, which are related to
the topics covered in the lectures.
During the semester additional practice problems will be given
to you to get prepared for your mid-term and final exams.
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What to do to Succeed in this course?
Attend the classes on time and regularly.
Do not miss any random quizzes
Use your text book extensively
Find out what exactly has been covered in lectures, which you have missed.
Study the materials given in the lectures thoroughly and continuously
Visit the course web page on the Blackboard regularly to get information
regarding lecture notes, course calendar, solutions to problems, tests, and etc.
Solve a lot of problems from your text book, other references, and any other
sources you can find on the Internet