Table Of ContentWoodheadPublishingSeriesin
CompositesScienceandEngineering
DAMPING IN FIBER
REINFORCED
COMPOSITE MATERIALS
PRAMODKUMAR
Assoc.Professor,Dr.BRAmbedkarNationalInstituteofTechnology(NIT)
Jalandhar,Punjab,India
S.P.SINGH
Professor,DepartmentofMechanicalEngineering,IndianInstituteof
TechnologyDelhi,HauzKhas,NewDelhi,India
SUMITSHARMA
AssistantProfessor,Dr.BRAmbedkarNationalInstituteofTechnology(NIT)
Jalandhar,Punjab,India
Editor-in-Chief
ProfessorCostasSoutis
HeadofAerospaceEngineering,UniversityofManchester,UK
SeriesEditors
ProfessorAdrianMouritz
ExecutiveDean,RMIT,Australia
ProfessorSureshAdvani
Assoc.Director,CentreforCompositeMaterials,Univ.Delaware,USA
ProfessorBodoFiedler
DirectorInst.PlasticsandComposites,TUHamburg,Germany
ProfessorLeifAsp
DivisionofMaterialsandComputationalMechanics,Chalmers,Sweden
ProfessorYurisA.Dzenis,R.VernonMcBroom
ProfessorofEngineering,DepartmentofMechanicalandMaterialsEngineering
UniversityofNebraska-Lincoln,USA
ProfessorChunH.Wang
HeadofSchoolofMechanicalEngineering,UNSW,Australia
DAMPING IN FIBER
REINFORCED
COMPOSITE MATERIALS
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ISBN:978-0-323-91186-3
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Contents
Preface vii
1. Introduction 1
1.1 Objectiveofthebook 3
1.2 Outlineofbook 4
References 5
2. Methodsofmodelingdamping 7
2.1 Introduction 7
2.2 Macromechanicalapproach 12
2.3 Micromechanicalapproach 18
2.4 Nonlineardamping 30
2.5 Conclusion 36
References 37
3. Measurementofdamping 45
3.1 Measurementofdampingfromdecayplot 45
3.2 Ageneralizedmethodoffindingdamping 47
3.3 Multimodeevaluationofdamping 49
3.4 Dampingratiofordifferentmodesofdeformation 51
3.5 Resonalysermethodofevaluationofdampingcoefficientmatrix 53
3.6 Frequencydependenceofdamping 54
3.7 Concludingremarks 54
References 55
4. Micromechanicalstudyoftwo-phasecomposite 57
4.1 Micromechanicalmodels 57
4.2 Fiberpackinggeometry 65
4.3 Finiteelementapproach 69
4.4 Mathematicalmodelforfrequencydependence 74
4.5 Resultsanddiscussions 76
4.6 Conclusion 95
References 96
5. Modelingofthreephasecomposite 99
5.1 Mathematicalmodelingofthreephasecomposite 99
v
vi Contents
5.2 Finiteelementsmodel 104
5.3 Frequencydependenceofthreephasecomposite 106
5.4 Resultsanddiscussion 106
5.5 Conclusion 124
References 125
6. Modelingofnonlineardamping 127
6.1 Introduction 127
6.2 Mathematicalmodel 128
6.3 Resultsanddiscussions 132
6.4 Conclusion 138
References 139
7. Applicationsofdampingandprinciplesofvibrationcontrol 141
7.1 Applicationsofdamping 141
7.2 Principlesofvibrationcontrol 151
References 159
Index 161
Preface
The primary audience targeted for this book include researchers working
in the area of damping in composite materials.Currently,no book on the
market explains the basics of damping in composites.The proposed book
will cover the basics of damping in composites,and modeling (in Matlab),
as well as in FEM.The book will also include the basics of the dynamic
behavior of composites and will explain the use of a dynamic mechanical
analyzerinpredictingdampingincomposites.Peopleworkinginthefieldof
mechanical engineering,industrial engineering,biotechnology,and physics
will find this book useful in predicting the damping behavior of fibrous
composites.Furthermore,thebookcanbeusedasatextbookon“Damping
in Composites”for postgraduate and doctorate-level students.Those who
wanttolearnmoreaboutthebasicsofdampingincompositeswillfindthis
book extremely helpful,as there is no other book published on this topic.
Damping is an important parameter for measuring and predicting the
dynamicperformance ofcompositematerials.Inthisexemplarynewbook,
the authors discuss damping behavior in fiber-reinforced composites.Di-
vided into 7 main chapters, the book starts with an introduction to the
basic concepts of damping in composite materials. Methods of modeling
damping are then discussed in chapter 2. These include both macro and
micro-mechanical approaches.Chapter 3 deals with experimental methods
for measuring damping. The decay plot and circle methods have been
discussedindetail.Inchapter4,aparametricstudyofatwo-phasecomposite
materialispresentedusingdifferentmicromechanicalmodels,suchasunified
micromechanics, and Hashin Eshelby’s to predict elastic moduli and loss
factors. A bridging model that incorporates the effect of fiber packaging
factors is then compared to FEM results.Chapter 5 investigates the effect
of the interphase on the mechanical properties of the composite.A mathe-
matical model is developed for the prediction of elastic moduli of a three-
phase fiber-reinforced composite. Chapter 6 presents a nonlinear model
for the prediction of damping in viscoelastic materials. The final chapter
looks at some of the main engineering applications of damping in real life
and principles of vibration control. The readers will be able to infer the
vii
viii Preface
importance of damping and principles of vibration control in FRPs after
reading this chapter.
The book will be an essential reference resource for academic and
industrialresearchersworkinginthefieldofcompositematerials,especially
damping behavior.
Pramod Kumar
Assoc.Professor,Dr.B.R.Ambedkar National Institute of Technology
Jalandhar,Punjab,India
S.P.Singh
Professor,Department of Mechanical Engineering,
Indian Institute of Technology Delhi,
Hauz Khas,New Delhi
India
Sumit Sharma
Assistant Professor,Dr.B.R.Ambedkar National Institute of Technology
Jalandhar,Punjab,India
June 2022
CHAPTER 1
Introduction
Astructuralcompositeisamaterialsystemconsistingoftwoormorephases
on a macroscopic scale whose mechanical performance and properties are
designedtobesuperiortothoseoftheconstituentmaterialsactingindepen-
dently.One of the phases is stiffer and stronger and is called reinforcement
and the less stiff and weaker phase is known as matrix.Because of chemical
interaction or other processing effects, an additional distinct phase called
interphase exists between the reinforcement and matrix. The properties
of composite materials depend on the properties of its constituent, their
geometry,andthedistributionofthephases.Thepropertiesofthecomposite
materials combine the best features of each constituent to maximize a
given set of properties, that is, stiffness, strength-to-weight ratio, tensile
strength, and minimize others, such as weight and cost. Composites have
auniqueadvantageovermonolithicmaterials,suchashighspecificstrength,
high specific stiffness, tailored damping, and adaptability to the intended
function of the structure. These materials are being used extensively for
varioushightechnologyapplications,suchasspacecraftandaircraftstructural
components,gasturbines,marine,andautomobileapplications.Theendless
research for reliable and low-cost structural and material system resulted in
inexpensivefabricationmethods,whichhavemadecompositesaffordableto
several appliances.
POLYMER-MATRIXcomposites(PMCs)andmetal-matrixcompos-
ites (MMCs) are two of the broad categories of composite materials in
terms of matrix classification.PMCs are typically used in low-temperature
structural applications,such as in civil structures,biomedical implants,au-
tomobiles,and airframe structures.The fibers typically provide the stiffness
and strength to the composite and can be made from a wide variety of
materials,includingglass,graphite,Kevlar,andboron,asexamples.Thefibers
canbearrangedinalmostanyfashion,rangingfromtotallyrandomtohighly
structuredandorganized.InMMCs,thematrixphaseconsistsofcontinuous
metallic material,such as aluminum,titanium,magnesium,copper,etc.The
reinforcing constituent is normally ceramic (e.g., silicon carbide, silicon
nitride,alumina).MMCsareusedintheaerospaceindustryforairframeand
spacecraftstructures,aswellasintheautomotive,electronic,andevenleisure
DampinginFiberReinforcedCompositeMaterials. Copyright©2023ElsevierLtd.
DOI:https://doi.org/10.1016/B978-0-323-91186-3.00004-6 Allrightsreserved. 1
