01 Vibrations Lecture 1

7/25/2019 01 Vibrations Lecture 1

1/51

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.


2/51

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


3/51

Monochord

3MECE 3210 Mechanical Vibrations Lecture # 01


4/51

Pendulum Vibration Process

4

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

MECE 3210 Mechanical Vibrations Lecture # 01


5/51

Why we need to study mechanical vibrations?

5

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.



6/51

Undesired Mechanical Vibrations



7/51

Undesired Mechanical Vibrations



8/51

Desired Mechanical Vibrations



9/51

Terminology

9

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)



10/51

10

Mass-Spring-Damper Model

M

()

()

The amplitude (A) of a vibrating mass (system) defines itsmaximum displacement from its equilibrium position



11/51

Pendulum Vibration Process

11

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



12/51

Mass-Spring-Damper Models



13/51

Mass-Spring Model

13

m

mg



14/51

14

m

Mass-Spring Model



15/51

15

m

Mass-Spring Model



16/51

16

m

Mass-Spring Model



17/51

17

m

Mass-Spring Model



18/51

18

m

Mass-Spring Model



19/51

19

m ()mg

= sin( + )

Maximum Amplitude

(/)= 2 ()

Phase (rad)

()

= 0

Mass-Spring Model



20/51

20

()

= 0

2

= 2. =

.

Mass-Spring Model



21/51

21

()

2

M N

2

L

2

Mass-Spring Model



22/51

22

()

Mass-Spring Model



23/51

Vibration and Fugue



24/51

24

Vibration and Fugue



25/51

Fugue-Modeling

25

m

()mg



26/51

26

m

mg

Fugue-Modeling



27/51

27

m

Fugue-Modeling



28/51

28

m

Fugue-Modeling



29/51

29

m

Fugue-Modeling



30/51

30

m

Fugue-Modeling



31/51

31

m

Fugue-Modeling



32/51

32

m

Fugue-Modeling



33/51

33

m

Fugue-Modeling



34/51

34

m

()mg

Fugue-Modeling



35/51

35

m

()mg

Fugue-Modeling



36/51

36

m

Fugue-Modeling

MN


Mass Spring Damper Models


37/51

Mass-Spring-Damper Models

37

()

2

M N



38/51

38

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.



39/51

39

Prerequisites

ENGR 2020 - STATICS AND DYNAMICS [Min Grade: D]

OR

ENGR 2430 - DYNAMICS [Min Grade: D]

OR

MECE 2430 - DYNAMICS [Min Grade: D]



40/51

40

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



41/51

41

Required Course Text

Mechanical Vibrations, Fifth Edition,

S.S. Rao, Prentice Hall, 2011, ISBN:

013-212819-3.



42/51

42

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



43/51

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



44/51

TAs Information

44

Name Nadim Arafa Omar Sadek

Email [email protected] [email protected]

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.

mailto:[email protected]:[email protected]:[email protected]:[email protected]


45/51

Final Grade Breakdown

45

Assignments: 10%

Laboratories: 10%

In class Quizzes: 5% (bonus)

Midterms: 30%

Exam: 50%



46/51

Midterm Exam

46

Midterm Date:

Friday, March 4, 2016 - 05:10 PM to 06:30 PM

Midterm Location:

Library Portables UL11



47/51

Lab Description

47

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



48/51

Computer Experience

48

MATLAB will be used in solving problems

throughout the course.

Problems solved by MATLAB must be shown

in full with the steps taken.



49/51

Assignments

49

There are five sets of assigned homework placed in the


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.



50/51

Assignments

50

There are five sets of assigned homework placed in the


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.



51/51

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

Date post:	24-Feb-2018
Category:	Documents
Upload:	cody-walton
View:	214 times
Download:	0 times

01 Vibrations Lecture 1

Documents