Nonlinear Approaches in Engineering Applications: Applied Mechanics, Vibration Control, and Numerical Analysis

340 Pages·2015·11.01 MB·English

by  Liming Dai

Liming Dai · Reza N. Jazar Editors
Nonlinear
Approaches in
Engineering
Applications
Applied Mechanics, Vibration Control,
and Numerical Analysis
Nonlinear Approaches in Engineering Applications

Liming Dai • Reza N. Jazar
Editors
Nonlinear Approaches
in Engineering Applications
Applied Mechanics, Vibration Control,
and Numerical Analysis
123
Editors
LimingDai RezaN.Jazar
DepartmentofIndustrial SchoolofAerospace,Mechanical
SystemsEngineering andManufacturingEngineering
UniversityofRegina RMITUniversityBundooraEastCampus
Regina,SK,Canada Bundoora,VIC,Australia
ISBN978-3-319-09461-8 ISBN978-3-319-09462-5(eBook)
DOI10.1007/978-3-319-09462-5
SpringerChamHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2014953220
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Preface
This book follows the same concept of the first two volumes and is based on the
ASME 2013 and 2012 Congress in the track of Dynamics Systems and Control,
OptimalApproachesinNonlinearDynamics,whichwereorganizedbytheeditors.
The nonlinear approaches and techniques have been developed since decades ago.
Theresearchonnonlinearscienceanddynamicshavebroughtnewinsightsintoour
modelingmethodsofnaturalandengineeringphenomena.Althoughmanyofthese
approaches and techniques have been brought into research and engineering prac-
tices,linearizationandsimplificationarestillthedominatingapproachesexistingin
physicsandengineering.Natureisnonlinearingeneralastheresponsesofphysics
and engineering systems are nonlinear. Linearization ends up with simplification,
and it damages the original characteristics of the systems. Such simplifications
usually lead to inaccuracy, misunderstanding, or even incorrect conclusions. For
example, Hooke’s law including the generalized Hooke’s law is linear and it
composes the foundation of linear elasticity and dominates numerous solutions
of physical systems and mechanical designs. However, no material is perfectly
linear.Anymaterialusedintherealworldcanactuallybeanonlinearandcomplex
system, not only due to its material or structure nonlinearity but also due to the
inhomogeneousnessandanisotropyofthematerials.
Anotherchallengefacingthescientistsandengineersinourtimeisthegeneration
of the solutions and characterization of the nonlinear systems modeled from the
physicalsystemsinreality.Itwouldbegreatlybeneficialinaccuratelyevaluatingthe
behaviorofnonlinearsystemsandrevealingtheactualnatureofthesystems,with
utilizationoftheexistingmathematicaltoolsandanalyticalmeans,iftheanalytical
solutions of nonlinear systems could be pursued. Due to the nonlinearity and
complexityofthenonlinearsystems,unfortunately,itisverydifficultorimpossible
to derive the analytical and closed-loop solutions for the systems. In solving or
simulatingthenonlinearsystems,onemayhavetorelyonapproximateornumerical
methods, which may only provide approximate results for the systems while
errors are unavoidable during the processes of generating the approximate results.
vii
viii Preface
Approximation and inaccuracy are the inescapable shadows following the current
researchandengineeringpracticesinvolvingnonlinearityornonlinearsystems.
Intheroleoftheeditorsaswellasthechaptercontributorsofthisbook,wehave
tried to present a collection of chapters showing the theoretically and practically
sound nonlinear approaches and their engineering applications in various areas, in
hoping that this book may provide useful tools and comprehensible examples of
solving,modeling,andsimulatingthenonlinearsystemsexistingintherealworld.
Thecarefullyselectedchapterscontainedinthepresentbookreflectrecentadvances
in nonlinear approaches and their engineering applications. The book intends to
featureinparticularthefundamentalconceptsandapproachesofnonlinearscience
and their applications in engineering and physics fields. It is anticipated that this
book may help to promote the development of nonlinear science and nonlinear
dynamics in engineering, as well as to stimulate research and applications of
nonlinear science and nonlinear dynamics in physics and engineering practices. It
isalsoexpectedthatthebookwillfurtherenhancethecomprehensionofnonlinear
scienceandstimulateinteractionsamongscientistsandengineerswhoareinterested
innonlinearscienceandwhofindthatnonlinearityandcomplexityofsystemsplay
animportantroleintheirrespectivefields.
Withthethemeofthebook,nonlinearapproachesandengineeringapplications:
Applied Mechanics, Vibration Control and Numerical Analysis, the book covers
interdisciplinary studies on theories and methods of nonlinear science and their
applications in complex systems such as those in nonlinear dynamics, vehicle
dynamics, rigid body, solid mechanics, safety, visco-elastic mechanics, control
engineering, ocean engineering, mechatronic engineering, acoustic engineering,
andmaterialscience.Examplesinclude:steady-statedynamicanalysisofvehicles;
rigid body dynamics and Razi acceleration discussion; a deep discussion about
piecewise linear vibration isolators and challenges in discovering its time and
steady-state determination; active vibration control for axially translation cables
to limit their vibrating reactions; a new numerical solution method for ordinary
differential equations where other methods fail; visco-elastic materials analysis
anddeterminationoftheirlosstangent;investigationonthefrontalhuman-vehicle
impactandre-designingthehoodofthecartosavepedestrians;anewtreatmentand
analysis of the post-bukling of thin tube structures; study in acoustics of exhaust
system to reduce their noise; parametric segmentation of nonlinear structures in
imagedata;predictionandanalysisofsealevel.
Level ofthe Book
This book aims at engineers, scientists, researchers, engineering and physics
studentsofgraduatelevels,togetherwiththeinterestedindividualsinengineering,
physics,andmathematics.Thischapter-bookfocusesonapplicationofthenonlinear
approachesrepresentingawidespectrumofdisciplinesofengineeringandscience.
Throughout the book, great emphases are placed on engineering applications,
Preface ix
physical meaning of the nonlinear systems, and methodologies of the approaches
in analyzing and solving for the systems. Topics that have been selected are of
high interest in engineering and physics. An attempt has been made to expose the
engineersandresearcherstoabroadrangeofpracticaltopicsandapproaches.The
topics contained in the present book are of specific interest to engineers who are
seekingexpertiseinnonlinearanalysis,mathematicalmodelingofcomplexsystems,
optimization of nonlinear systems, non-classical engineering problems, and future
ofengineering.
The primary audience of this book is the researchers, graduate students and
engineers in mechanical engineering, engineering mechanics, electrical engineer-
ing,civilengineering,aerospaceengineering,oceanengineering,mathematics,and
science disciplines. In particular, the book can be used as a book for the graduate
students as well as senior undergraduate students to enhance their knowledge by
taking a graduate or advanced undergraduate course in the areas of nonlinear
science, dynamics and vibration of discrete and continuous system, structure
dynamics,andengineeringapplicationsofnonlinearscience.Itcanalsobeutilized
as a guide to the readers’ fulfilment in practices. The covered topics are also of
interesttoengineerswhoareseekingtoexpandtheirexpertiseintheseareas.
Organizationofthe Book
The main structure of the book consists of two parts of analytical and practical
nonlinearity, including 12 chapters. Each of the chapters covers an independent
topicalongthelineofnonlinearapproachandengineeringapplicationsofnonlinear
science. The main concepts in nonlinear science and engineering applications are
explained fully with necessary derivatives in detail. The book and each of the
chaptersisintendedtobeorganizedasessentiallyself-contained.Allnecessarycon-
cepts, proofs, mathematical background, solutions, methodologies and references
are supplied except for some fundamental knowledge well known in the general
fieldsofengineeringandphysics.Thereadersmaythereforegainthemainconcepts
ofeachchapterwithaslessaspossibletheneedtorefertotheconceptsoftheother
chapters.Readersmayhencestarttoreadoneormorechaptersofthebookfortheir
owninterests.
Method ofPresentation
Thescopeofeachchapterisclearlyoutlinedandthegoverningequationsarederived
withanadequateexplanationoftheprocedures.Thecoveredtopicsarelogicallyand
completelypresentedwithoutunnecessaryoveremphasis.Thetopicsarepresented
inabookformratherthaninthestyleofahandbook.Tables,charts,equations,and
referencesareusedinabundance.Proofsandderivationsareemphasizedinsucha