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Structural Dynamics - ESA 322Vibration - EMM 342

Dr. Norizham Abdul Razak

University Science of Malaysia

norizham@usm.my

February 22, 2015

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Course Information

This course is divided into two parts

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Course Outcomes

At the end of this course you should be able to:

1. Determine vibration response for a 1 degree-of-freedom (dof)system. I.e., students should understand the response in termsof the displacement, velocity, and acceleration.

2. Able to calculate natural frequencies and mode for 2DOFsystem and MDOF.

3. Able to design a tuned vibration absorber (dynamic vibrationabsorber) system.

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Course Assessments

1. Final exam - 60%I Vibration - Final exam - 30%I Vibration - Final exam questions - 3

2. Total coursework - 40%I Vibration - Coursework - 20%

Vibration coursework assesments - 20%

Assessment type % Value

Test 1 30.0 6

Project 30.0 6

Quizzes 15.0 3

Assignments 15.0 3

Attitudes 10.0 2

Total 100 20

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Rules

Obey

1. Do your own assignments

2. Those who skip classes will be barred from the final exam

3. Do not be late. Doors will be locked after 10 minutes

4. Turn off/ silence your electronic gadgets (mobilephones/tablets/laptops)

5. Keep your electronics gadgets in your bag

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General Info

1. Lecture times

Monday 9:00 to 10:00Wednesday 9:00 to 11:00

2. Where to find me : Aero building, room number : 236

3. My email : norizham@usm.my

4. My extension : 5909

I will be at my office during these times

Consultation times

Monday 2:30 to 4:30Tuesday 10:30 to 12:30Thursday 10:00 to 12:00

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Topics that will be covered

1. Introduction to vibrationi Definition of vibrationii Classification of Vibrationiii Vibration terminologyiv Vibration elementsv Vibration analysis procedure

2. Single degree of freedom systemi Free undamped vibrationii Free damped vibration (Viscous damping)iii Free undamped force vibrationiv Free damped force vibration

3. Two degree of freedom system

4. Dynamic vibration absorber

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Schedule

Week 1 Introductory classIntroduction to Vibration

Week 2 SDOF Free vibrationSDOF Damped vibration

Week 3 SDOF Undamped Forced VibrationSDOF Damped Forced Vibration

Week 4 SDOF Base ExcitationSDOF Rotating Unbalanced Mass

Week 5 System Identification2DOF Free Vibration

Week 6 2DOF Forced VibrationDynamic vibration absorber

Week 7 Test 1

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References

1. Booksi S. S. Rao, Mechanical Vibrations, Pearson/Prentice Hall, 2004ii R. F. Steidel Jr, An Introduction to Mechanical Vibrations, John

Wiley & Sons. (Latest Edition)iii R. C. Hibbeler, Engineering Mechanics: Dynamics, Prentice

Hall, (Latest Edition; Chapter 22)iv J. L. Meriam and L. G. Kraige, Engineering Mechanics:

Dynamics, John Wiley and Sons. Latest Edition.

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Motivation

As engineers, why do we need to learned structural dynamics

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Lecture1_F16_1.aviMedia File (video/avi)

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Motivation

As engineers, why do we need to learned structural dynamics

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Motivation

There are good and bad vibrations

Good Vibration

I Mobilephone

I Jackhammer

I Exercise equipments

I Concrete

I Vibration shaker

Bad Vibration

I Car engine

I Aircraft structure

I High precision machine

I Swaying in building

I Grass trimmer

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Motivation

As engineers, why do we need to learned structural dynamics

Vibrations in machines and structures are typically undesirable asthey produce stresses, energy losses and increased bearing loads.They contribute to structural wear and can lead to passengerdiscomfort in vehicles.

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Introduction

What is the definition of vibration:

I Usually understood as oscillation between an equilibrium pointI Any motion that repeats itself after an interval of time is

called vibration or oscillationI Can be viewed as the flow between kinetic energy and

potential energy

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Classification of Vibration:

Vibration can be classified as

I Free vibration

I Force vibration

I Damped vibration

I Undamped vibration

I Linear vibration

I Non-linear vibration

I Deterministic vibration

I Random Vibration (undeterministic) vibration

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Classification of Vibration: External Force

Free Vibration

I Vibrate on its own

I No external force acts onthe system

Forced Vibration

I Subjected to an externalforce

I Often a repeating type offorce

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Classification of Vibration: Damping

Undamped Vibration

I If no energy is lost ordissipated

I Amplitude is maintained

I Not physical

Damped Vibration

I Energy is lost throughresistance

I E.g. friction

I Physical

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Classification of Vibration: Linearity

Linear VibrationAll components such as thespring mass and damper behavelinearly.

Nonlinear VibrationIf one or more components of asystem are not linear then thesystem is nonlinear.

Example of linear and nonlinear stiffness

0.5 0.4 0.3 0.2 0.1 0 0.1 0.2 0.3 0.4 0.52.5

2

1.5

1

0.5

0

0.5

1

1.5

2

2.5

Angle, rad

To

rqu

e,

Nm

Case A Linear pitch

Case B Nonlinear pitch

Case C Nonlinear pitch

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Classification of Vibration: Input

Deterministic Vibration

If the value or magnitude of theexcitation acting on a system isknown at any given time.

Undeterministic Vibration

When the value of excitation atany given time cannot bepredicted or known

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Vibration Terminology

Frequency :

I Cycle per second

I Unit : Hz or rad/s

I f = 1T Hz

I = 2f rad/s

Amplitude:

I Distance moved by apoint on a vibratingbody

I measured from itsequilibrium position

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Vibration Terminology

Degree of freedom:The number of independent co-ordinates required to describe themotion of a system. System with a finite number of degrees offreedom are called discrete or lumped parameter system Thosewith an infinite number of degrees of freedom are calledcontinuous or distributed systems.

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Vibration Terminology

Periodic motion:Defined as any motion that repeats after equal intervals of time

Periodic Signal

Aperiodic Signal

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Vibration Terminology

Example of periodic motion

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Vibration Elements

Vibration exist when it has

I A means of storing potential energy (Spring or elasticity)

I A means of storing kinetic energy (mass or inertia)

I A means by which energy is gradually lost (damper)

The forces acting on the vibrating systems are usually

I External forces (Mechanical/Aerodynamic/Hydrodynamic)

I Restoring force (Stiffness)

I Inertia force (mass /moment of inertia)

I Damping force (viscous, coulomb or hysteretic)

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Example of Vibration Elements

Periodic Signal

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Study Guide

Given a problem

I You should know how to draw a free body diagram of aparticle, i.e., a body with 1 DOF. The FBD should be aseparate diagram from the schematic diagram

I Clearly label the forces on the and body and the coordinate(positive direction) of the body

I Show the EOM from Newtons Second Law

I Write the final answer of the EOM in terms of the values ofthe coefficients if m, k, c are given

I Keep numerical values in 2 significant figures in test/problemsand 3 significant figures in homework problems

I Draw a box around your final answer

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Questions?

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Next class will be on Wednesday 9:00 a.m.

Thank You

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