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 ©SpringerInternationalPublishingSwitzerland2015 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. 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Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) DedicatedtoXinmingandMojgan. 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