Solid Mechanics and Its Applications Series Editor: G.M.L. Gladwell Seyed Habibollah Hashemi Kachapi Davood Domairry Ganji Dynamics and Vibrations Progress in Nonlinear Analysis Solid Mechanics and Its Applications Volume 202 Series Editor G. M. L. Gladwell Department of Civil Engineering, University of Waterloo, Waterloo, Canada For furthervolumes: http://www.springer.com/series/6557 Aims and Scope of the Series Thefundamentalquestionsarisinginmechanicsare:Why?How?andHowmuch? The aim of this series is to provide lucid accounts written by authoritative researchersgivingvisionandinsightinansweringthesequestionsonthesubjectof mechanicsas itrelatesto solids. The scope of the series covers the entire spectrum of solid mechanics. Thus it includes the foundation of mechanics; variational formulations; computational mechanics;statics,kinematicsanddynamicsofrigidandelasticbodies:vibrations of solids and structures; dynamical systems and chaos; the theories of elasticity, plasticity and viscoelasticity; composite materials; rods, beams, shells and mem- branes; structural control and stability; soils, rocks and geomechanics; fracture; tribology; experimental mechanics; biomechanics and machine design. The median level of presentation is the first year graduate student. Some texts aremonographsdefiningthecurrentstateofthefield;othersareaccessibletofinal year undergraduates; but essentially the emphasis is on readability and clarity. Seyed Habibollah Hashemi Kachapi Davood Domairry Ganji Dynamics and Vibrations Progress in Nonlinear Analysis 123 Seyed HabibollahHashemi Kachapi DavoodDomairry Ganji Department of Mechanical Engineering Department of Mechanical Engineering Babol Universityof Technology Babol Universityof Technology Babol Babol Iran Iran ISSN 0925-0042 ISBN 978-94-007-6774-4 ISBN 978-94-007-6775-1 (eBook) DOI 10.1007/978-94-007-6775-1 SpringerDordrechtHeidelbergNewYorkLondon LibraryofCongressControlNumber:2013944670 (cid:2)SpringerScience+BusinessMediaB.V.2014 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionor informationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purposeofbeingenteredandexecutedonacomputersystem,forexclusiveusebythepurchaserofthe work. Duplication of this publication or parts thereof is permitted only under the provisions of theCopyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the CopyrightClearanceCenter.ViolationsareliabletoprosecutionundertherespectiveCopyrightLaw. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexempt fromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. While the advice and information in this book are believed to be true and accurate at the date of publication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityfor anyerrorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,with respecttothematerialcontainedherein. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface Introduction Dynamical and vibratory systems are basically applications of mathematics and science to the solution of real-world problems. In the majority of real-life and applied phenomena in engineering sciences, as well as in a multiplicity of other sciences,solutions ofspecificallydefined problemsare theultimategoal.Inorder to apply engineering or any other science, it is necessary to fully understand dynamical and vibratory systems and how to solve cases of either linear or non- linear equations using analytical and numerical methods. It is of particular importance to study nonlinearity in dynamics and vibration, because almost all applied processes act nonlinearly. In addition, nonlinear analysis of complex systems is one of the most important and complicated tasks, especially in engi- neering and applied science problems. There are only a handful of books that focus on nonlinear dynamics and vibrations analysis. Some of these books are written at a fundamental level that maynotmeetambitiousengineeringprogramrequirements.Othersarespecialized incertain fieldsofoscillatorysystems,including modelingandsimulation.Inthis book, we attempt to strike a balance between theory and practice, fundamentals and advanced subjects, and generality and specialization. Noneofthebooksinthisareahavecompletelystudiedandanalyzednonlinear equations in dynamical and vibratory systems using the latest analytical and numerical methods, which, if included, would allow the user to solve problems without needing to study many different references. Therefore, in this book, we havechosentousethelatestanalyticandnumericallaboratorymethods,referring to a bibliography of more than 300 books, papers, and research reports, many of them written by the authors of this book, and to consider almost all possible processes and physical configurations, thereby exploring new theories that have been proposed to solve real-life problems in engineering and applied sciences. In this way, the users (bachelor’s, master’s, and Ph.D. students, university teachers, and even workers in research centers in different fields of mechanical, civil, aerospace, electrical, chemical, applied mathematics, physics, etc.) can approach such systems with confidence. In the different chapters of the book, not only are v vi Preface linear and nonlinear problems, especially those in an oscillatory form, broadly discussed, but also applied examples are solved in a practical manner by the proposed methodology. An abundant number of examples and homework problems are provided. The users of this collection can achieve very strong capabilities in the area, especially ofnonlinear phenomena indynamically andvibratorysystems, such as the following: • A complete understanding of the nonlinearity sources and formulation of dynamicalmotionequationsindifferentsystemsusingthemostgeneralmethods (e.g., principle of virtual work, D’Alembert’s principle, Newton and Lagrange methods, etc.). • A complete understanding of the fundamentals of oscillatory systems and their governingnonlinearequations;alsoanalyticalandnumericalmethodsinsolving applied problems, especially those with nonlinearities. • A complete study of mathematical problems in engineering, analytic, and numeric methods (e.g., perturbation methods, the homotopy perturbation method, variational methods, energy methods, limit cycles, the parameterized perturbation method, the singular perturbation method, Adomian’s decomposi- tion method, the differential transformation method and its modification, He’s parameter expansion method, He’s amplitude–frequency formulation, the har- monic balance method, the coupled method of homotopy perturbation, the variational method, Floquet theory, etc.). • Complete familiarity with specialized processes and applications in different areasofthefield,studyingthem,eliminatingcomplexitiesandcontrollingthem, and also applying them in real-life engineering cases. • A complete analysis of important engineering systems (e.g., NDOF systems, discs, springs, beams, normal modes, multibody phenomena, shafts, sliders, the human body, nonlinear oscillators in automobile design, rotating rigid frames, flexiblebeams,rotatingrigidhubs,elasticcantileverbeams,thehumaneardrum, etc.). • Acompleteanalysisofimportantequationsinthefieldandtheirgeneralizations in real-life applications with practical examples (Duffing’s oscillation, Van der Pol’s oscillation, Mathieu’s oscillation, Hamiltonian oscillation, Hill’s oscilla- tion, resonances, viscoelasticity, damping, fraction order, cubic nonlinearity, coupled systems, wave equations, etc.). • Theabilitytoencounter,model,andinterpretanengineeringprocessorsystem and to solve the related complexities engendered by the vibrations property in linear and nonlinear cases. Preface vii Audience This book is a comprehensive and complete text on dynamical and vibratory motions and analytical and numerical methods in applied problems. It is self- contained, and the subject matter is presented in an organized and systematic manner.Thisbookisquiteappropriateforseveralgroupsofpeople,includingthe following: • Senior undergraduate and graduate students taking courses in the mentioned fields. • Professionals, for whom the book can be adapted for a short course on the subject matter. • Design and research engineers, who will be able to draw upon the book in selecting and developing mathematical models for analytical and design pur- poses in applied conditions. • Practicingengineersandmanagerswhowanttolearnaboutthebasicprinciples andconceptsinvolvedinthesolvingofproblemsusinganalyticalandnumerical methods such as dynamics, vibrations, and systems analysis and how they can be applied at their own workplaces. • Generally, users who are bachelor’s, master’s, and Ph.D. students, university teachers, andeven researchersatcentersindifferentfields ofmechanical,civil, aerospace engineering, applied physics, mathematics, and so forth. Becausethebookisaimedatawideaudience,thelevelofmathematicsiskept intentionally low. All the principles presented in the book are illustrated by numerous worked examples. The book draws a balance between theory and practice. Acknowledgments We are grateful to all those who have had a direct impact on this work. Many people working in the general areas of nonlinear phenomena, vibrations, oscilla- tions, dynamics, mathematical, and physical problems, and analytical and numerical methods have influenced the format of this book. The authors are very thankful to Babol Noshirvani University of Technology, Iran, and the National Elite Foundation of Iran (Bonyad Melli Nokhbeghan), Mazandaran Province, Sari, Iran, especially the nonlinear dynamics teams in the MechanicalEngineeringDepartment,andallprofessorsandstudentsofallIranian universities who helped them develop research skill, editing the electronic text, giving them useful consultation and precious guidance, and providing references for the authors, especially examples of applications that were used in different chapters. TheauthorsarethankfultotheMechanicalEngineeringDepartmentofFairfield University,USA,especiallydeceasedProf.RaoV.Dukkipati,andProf.Ji-HuanHe (Donghua University, Modern Textile Institute, Shanghai, China), and are espe- cially thankful to the Department of Mathematics of Saint Xavier University, Chicago, USA, and to Professor Abdul-Majid Wazwaz for helping them develop theirresearchskills,editingtheelectronictextandgivingusefulconsultations,and also for his precious guidance and for the references and lectures provided to the authors for use in different chapters. We are indebted to many colleagues and to numerous authors who have made contributionstotheliteratureinthisfield.Inaddition,Iamgreatlyindebtedtoall theauthorsofthearticleslistedinthebibliographyofthisbook,suchasProfessors Ali Nayfeh, Shaher Momani, Liao, G. Adomian, J. Srinivas, Richard H. Rand, Alexander Fidlin, and other professors for their kind and faithful support and references that were directly used in the writing of this book. I would also like to thankthereviewersfortheireffortsandfortheircommentsandsuggestions,which have well served to compile the best possible book for the intended and targeted audience. A special acknowledgment is expressed to the chief editor of the publisher for his excellent revision of the English language of the book and for editing the electronic text. ix x Acknowledgments Finally, we would very much like to acknowledge the devotion, encourage- ment, patience, and support provided by our family members. Iwouldappreciatebeinginformedoferrorsorreceivingothercommentsabout the book. Please write to the authors at the Babol Noshirvani University of Technologyaddressorsende-mailto:[email protected](SeyedH. Hashemi Kachapi) and ddg_davood@ yahoo.com (D. D. Ganji) We sincerely hope that the final outcome of this book will help students, researchers,andotherusersindevelopinganappreciationforthetopicofanalysis of nonlinear dynamical systems and nonlinear vibration analysis using analytical and numerical methods.