EXPERIMENTAL DETERMINATION OF DAMPING PROPERTY OF

STRUCTURE

DHARMA RAJ A/L KANAMUTHY

A project report submitted in partial fulfilment of the

requirements for the award of the degree of

Master of Science (Mechanical Engineering)

Faculty of Mechanical Engineering

Universiti Teknologi Malaysia

JANUARY 2017

iii

To my beloved wife and son

iv

ACKNOWLEDGEMENT

Thank you God for giving me the strength, ability and patience to complete

this project. I would also like to express my sincere appreciation and deepest

gratitude to the following individuals who had directly and indirectly support me

throughout this journey.

Firstly to my advisor, Prof. Ir. Dr. Roslan Abd Rahman for his continuous

guidance and encouragement, without which this work would not have been possible.

I am also extremely thankful to my parents for their prayers and support throughout

my study period. I thank profusely my colleagues for their help and cooperation

throughout this period.

A special thanks to my wife, Kathireen, who provided invaluable emotional

support during the many hours I spent working on this project. And last but not least,

to my nephew, Amiel Alroy Anthony, who always teased me for neglecting him but

who understood all along.

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ABSTRACT

The needs for reliable and accurate damping properties are necessary in order

to produce a good simulation and improve a major source of uncertainty at the design

stage. Thus, an experimental investigation was conducted to find damping property

of structure. In this study, three different plates were used to determine their

damping properties. Experimental modal analysis using impact hammer and

accelerometer was performed to acquire the frequency response function (FRF) of

test samples. Damping properties were extracted from FRF using polyreference

least-squares complex frequency-domain method (PolyMAX) and polyreference

least-squares complex exponential time-domain method (LSCE). The results reveal

that for lightly damped structure, the damping ratio from LSCE and PolyMAX are

comparable. However, for heavily damped structure, the damping ratio from LSCE

is slightly higher than damping ratio from PolyMAX. The results also show that

PolyMAX is better than LSCE in term of stabilisation diagram. Finally some

improvements on the experimental method have been proposed in order to achieve

accurate damping property.

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ABSTRAK

Keperluan untuk mendapatkan sifat resapan yang persis dan jitu adalah

mustahak untuk memperoleh simulasi yang tepat dan mengurangkan ketidakpastian

dalam proses rekabentuk. Oleh itu, eksperimen telah dijalankan untuk menentukan

sifat resapan struktur. Dalam ujikaji ini, tiga plat yang berbeza telah digunakan

untuk menentukan sifat resapannya. Eksperimen ujikaji modal telah dijalankan

untuk memperolehi data dalam bentuk fungsi tindak balas frekuensi (FRF). Sifat

resapan diperolehi melalui FRF dengan menggunakan kaedah “polyreference least-

squares complex frequency-domain method” (PolyMAX) dan “polyreference least-

squares complex exponential time-domain method” (LSCE). Hasil keputusan

menunjukkan bahawa untuk struktur yang rendah sifat resapan, nisbah resapan yand

diperolehi melalui LSCE dan PolyMAX adalah setanding. Walau bagaimanapun,

untuk struktur yang tinggi sifat resapan, nisbah resapan dari LSCE adalah sedikit

lebih tinggi dari PolyMAX. Hasil keputusan juga menunjukkan bahawa PolyMAX

lebih baik dari LSCE jika dibandingkan dari segi kestabilan. Akhir sekali, beberapa

ubahsuaian kepada kaedah eksperimen telah dicadangkan bagi memperolehi sifat

resapan yang lebih tepat.

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TABLE OF CONTENTS

CHAPTER TITLE PAGE

DECLARATION ii

DEDICATION iii

ACKNOWLEGEMENT iv

ABSTRACT v

ABSTRAK vi

TABLE OF CONTENTS vii

LIST OF TABLES x

LIST OF FIGURES xi

LIST OF SYMBOLS xiii

LIST OF APPENDICES xiv

1 INTRODUCTION 1

1.1 Introduction 1

1.2 Background of the Problem 1

1.3 Statement of the Problem 2

1.4 Objective 3

1.5 Research Question 3

1.6 Scope and Key Assumptions 3

1.7 Importance of the Project 4

1.8 Organization of the Report 4

1.9 Summary 5

2 LITERATURE REVIEW 6

2.1 Introduction 6

2.2 Review on previous studies 6

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2.3 Conclusion 10

3 BACKGROUND THEORY 11

3.1 Introduction 11

3.2 Modal Analysis 11

3.2.1 Spatial model 12

3.2.2 Modal model 12

3.2.3 Response model 13

3.2.4 Modal Testing 13

3.2.5 Modal Parameter Extraction 15

3.3 Summary 16

4 METHODOLOGY 17

4.1 Introduction 17

4.2 Research Framework 17

4.3 Instrument Selection 19

4.3.1 Accelerometer 19

4.3.2 Impact Hammer 20

4.3.3 LMS SCADAS Data Acquisition System 21

4.4 Measuring Method – Experimental Modal Analysis 22

4.4.1 Experiment Setup 23

4.4.2 Measurement Setup 24

4.4.3 Preparation of Samples 24

4.4.4 Experimental Procedure 26

4.5 Data Collection 28

4.6 Data Analysis 28

4.6.1 Finite Element Analysis 28

4.7 Overall Research Plan 29

4.8 Conclusion 31

5 RESULT AND DISCUSSION 32

5.1 Introduction 32

5.2 Determine Fixed Accelerometer Position 32

5.3 Mass Loading Effect due to Accelerometer 33

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5.4 Modal Analysis for Aluminium Plate 34

5.4.1 Natural Frequency 37

5.4.2 Damping Ratio 39

5.4.3 Mode Shape 41

5.5 Modal Analysis for Glass Fibre Composite Plate 44

5.5.1 Natural Frequency 46

5.5.2 Damping Ratio 48

5.6 Modal Analysis for Kevlar Fibre Composite Plate 49

5.6.1 Natural Frequency 52

5.6.2 Damping Ratio 54

5.7 Comparison between PolyMAX and LSCE 55

5.8 Summary 56

6 CONCLUSION AND RECOMMENDATION 57

6.1 Conclusion 57

6.2 Recommendation 57

REFERENCES 59

Appendices A - F 62 - 67

x

LIST OF TABLES

TABLE NO. TITLE PAGE

4.1 DYTRAN Accelerometer Specification 19

4.2 B&K Impact Hammer Specification 21

4.3 Measurement Setup 24

4.4 Research plan for Master Project 1 30

4.5 Research plan for Master Project 2 30

5.1 Natural frequency for aluminium plate (in hertz) 38

5.2 Natural frequency comparison for aluminium plate 38

5.3 Damping ratio for aluminium plate (in %) 40

5.4 Damping ratio comparison for aluminium plate (in %) 40

5.5 Natural frequency for glass fibre composite plate (in hertz) 47

5.6 Damping ratio for glass fibre composite plate (in %) 48

5.7 Damping ratio comparison for glass fibre composite plate (in %) 48

5.8 Natural frequency for Kevlar fibre composite plate (in hertz) 53

5.9 Damping ratio for Kevlar fibre composite plate (in %) 54

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LIST OF FIGURES

FIGURE NO. TITLE PAGE

4.1 Research Framework 18

4.2 DYTRAN Accelerometer Model 3225F1 19

4.3 B&K Impact Hammer 20

4.4 LMS SCADAS Mobile 22

4.5 Schematic of an experimental setup 23

4.6 Aluminium plate (487mm x 430mm x 2.48mm) 25

4.7 Glass fibre composite plate (380mm x 320mm x 3mm) 25

4.8 Kevlar fibre composite plate (380mm x 380mm x 2.3mm) 26

4.9 Experimental Setup 27

4.10 Finite Element Analysis steps 29

5.1 Driving point measurement 33

5.2 FRF relating to mass-loading effect 34

5.3 1st repeat of FRF measurement for aluminium plate 35

5.4 2nd

repeat of FRF measurement for aluminium plate 36

5.5 3rd

repeat of FRF measurement for aluminium plate 37

5.6 Natural frequency comparison for aluminium plate 39

5.7 Damping ratio comparison for aluminium plate 41

5.8 First mode shape for aluminium plate 42

5.9 Second mode shape for aluminium plate 42

5.10 Third mode shape for aluminium plate 43

5.11 Fourth mode shape for aluminium plate 43

5.12 1st repeat of FRF measurement for glass fibre composite plate 44

5.13 2nd

repeat of FRF measurement for glass fibre composite plate 45

5.14 3rd

repeat of FRF measurement for glass fibre composite plate 46

5.15 Natural frequency comparison for glass fibre composite plate 47

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5.16 Damping ratio comparison for glass fibre composite plate 49

5.17 1st repeat of FRF measurement for Kevlar fibre composite plate 50

5.18 2nd

repeat of FRF measurement for Kevlar fibre composite plate 51

5.19 3rd

repeat of FRF measurement for Kevlar fibre composite plate 52

5.20 Natural frequency comparison for Kevlar fibre composite plate 53

5.21 Damping ratio comparison for Kevlar fibre composite plate 54

5.22 Damping ratio difference between LSCE and PolyMAX 55

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LIST OF SYMBOLS

c - Damping coefficient

f - Force

k - Spring stiffness

m - Mass

C - Damping matrix

K - Stiffness matrix

M - Mass matrix

x - Displacement

x - Velocity

x - Acceleration

ω - Angular frequency

2

r - Eigenvalues

- Eigenvectors

jkH - Harmonic response in DOF j to a unit harmonic excitation applied in

DOF k

jX - Harmonic response in DOF j

kF - Harmonic excitation applied in DOF k

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LIST OF APPENDICES

APPENDIX TITLE PAGE

A Accelerometer Specification 62

B Impact Hammer Specification 63

C LMS SCADAS Mobile SCM01 Specification 64

D Modal Assurance Criterion for Aluminium Plate 65

E Modal Assurance Criterion for Glass Fibre

Composite Plate 66

F Modal Assurance Criterion for Kevlar Fibre

Composite Plate 67

CHAPTER 1

INTRODUCTION

1.1 Introduction

The chapter begins by reviewing background of the problem before move

into the problem statement. Then, the objective of the study and research question is

stated clearly. Next, the scope and key assumptions used in this study is clearly

defined. The importance of the study and the organization of this report are briefly

explained before summarizing this chapter at the end.

1.2 Background of the Problem

Vibration analysis represents an important research topic in the context of

structural and mechanical engineering. Most of the time, vibration is undesirable and

it is important to reduce it by dissipation its energy or damping.

Damping can be defined as the phenomenon by which mechanical energy is

dissipated in dynamic systems [1]. High energy dissipation will probably have low

vibration amplitudes. Damping is mostly associated with the change of mechanical

energy into thermal energy.

The recent developments in the fields of building structures have provided

motivation towards developing newer and more efficient materials which have

expedited the construction of lighter and more flexible buildings. These buildings

2

are known to be highly responsive to dynamic loadings [2]. Therefore it has become

more crucial to accurately determine dynamic properties which are the natural

frequencies and damping.

Besides that, in automotive industry, ride comfort is gaining more

prominence in recent years. Ride comfort can be defined as occupant’s overall

comfort and well-being during vehicle travel. Generally it involves all the vibration

phenomena which act on the occupants of a vehicle. Since the sources of the

vibration are outside of the passenger compartment, damping properties would help

to hinder the transmission of these disturbances into the passenger compartment area

[3].

In finite element analysis (FEA), the damping properties are important to

simulate responses and resulting spectra. This has been clearly seen in the case of

shock response spectrum where the amplitude is significantly affected by the

damping of the response.

Since the damping property cannot be deduced from other structural or

material properties, it becomes the most difficult dynamic property to predict at

design stage. Therefore the damping can be measured only by conducting dynamic

testing on a structure which is known as modal testing. The needs for reliable and

accurate damping properties are necessary to have in order to produce a good

simulation and improve a major source of uncertainty at the design stage.

1.3 Statement of the Problem

Since the damping properties are determined from modal parameter, the

accuracy of the measured data is of paramount importance in experimental modal

testing. The main challenge faced by many experiments in modal testing is the

variations in modal test data which may be obtained by using different measurement

techniques on a particular test structure [4]. Variations in modal test data have led to

inconsistency in determining damping values.

3

Typically, the modal parameter obtained from experimental modal analysis

may have low quality as a result of poor techniques and instrumentation used in the

measurement. The main disadvantage using accelerometer to measure the response

is due to mass loading effects. It is the mass relative to the effective mass of the

structure where it is mounted play often an important role. An accelerometer weight

at a very stiff location on a structure is different than that same accelerometer

mounted on a thin lightweight panel in the same structure. Besides that, mass

loading effects play a significant role when using a modal shaker [5].

The process of identifying modal parameters is commonly referred to as

curve fitting. Therefore the accuracy of estimation damping values are also depends

on which curve fitting technique is used. Part of this study involves in investigating

the variation in damping values using different curve-fitting techniques.

1.4 Objective

The research objective of the study is to identify the damping properties of

plates of several materials.

1.5 Research Question

The main research question is to determine which curve fitting algorithm is

suitable for all type of material.

1.6 Scope and Key Assumptions

The scope of this study is limited to:

Experimental approach using vibration technique.

4

Aluminium plate, glass fibre composite plate and Kevlar fibre

composite plate are used to identify the damping properties.

The boundary condition of the test samples are set to be free - free

condition.

Two curve fitting methods are used: polyreference least-squares

complex frequency-domain method (PolyMAX) and polyreference

least-squares complex exponential time-domain method (LSCE).

1.7 Importance of the Project

The contribution of this study is obvious as the resulting outcomes can be

capitalized as guidelines to achieve reliable and accurate damping properties which

will help to simulate dynamic response of structures.

1.8 Organization of the Report

This project report consists of six chapters; the first chapter gives an

overview of the subject by giving a background on the research subject and then

followed by a statement of the problem. The second chapter provides a detailed

review on the subject matter providing early literature to the very recent

developments in the research area. The third chapter explains the related theory

related to damping and modal analysis. Chapter four provides the methodology

which this research is conducted upon. Experimental results and discussion are

detailed in chapter five. Finally, chapter six concludes the study and provides

recommendation for future research.

5

1.9 Summary

One of the most effective ways to reduce vibration problem is to have

damping mechanism. The aim of the study is to determine reliable and accurate

damping properties.

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