Table Of ContentMechanisms and Machine Science 69
Juan Carlos Jauregui Editor
Nonlinear
Structural
Dynamics
and Damping
Mechanisms and Machine Science
Volume 69
Series Editor
Marco Cecarelli
LARM; Laboratory of Robotics and Mechatronics
DICeM; University of Cassino and South Latium
Cassino, Frosinone, Italy
Editorial Board Member
Alfonso Hernandez
MechanicalEngineering,UniversityoftheBasqueCountry,Bilbao,Vizcaya,Spain
Tian Huang
Department of Mechatronical Engineering, Tianjin University, Tianjin, China
Yukio Takeda
Mechanical Engineering, Tokyo Institute of Technology, Tokyo, Japan
Burkhard Corves
Institute of Mechanism Theory, Machine Dynamics and Robotics, RWTH Aachen
University, Aachen, Nordrhein-Westfalen, Germany
Sunil Agrawal
Department of Mechanical Engineering, Columbia University,
New York, NY, USA
This book series establishes a well defined forum for monographs, edited Books,
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(MechanismandMachineScience).Thefinalgoalisthepublicationofresearchthat
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More information about this series at http://www.springer.com/series/8779
Juan Carlos Jauregui
Editor
Nonlinear Structural
Dynamics and Damping
123
Editor
JuanCarlos Jauregui
Faculty of Engineering
AutonomousUniversity ofQueretaro
Querétaro, Mexico
ISSN 2211-0984 ISSN 2211-0992 (electronic)
Mechanisms andMachineScience
ISBN978-3-030-13316-0 ISBN978-3-030-13317-7 (eBook)
https://doi.org/10.1007/978-3-030-13317-7
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Preface
I want to thank all the contributors to this book for their patience and hard work.
ThisbookcompilessomeofthenewestresearchworkofthemembersofIFToMM
thatarepartoftheTechnicalCommitteeforVibrations(TC-Vibrations).Thisbook
came out as a joint effort to disseminate and share theoretical and experimental
researchinthefieldofvibrationsandtopromotetheworkdonebydifferentgroups
around the world. This book is a sample of various topics that the TC-Vibrations
groupareworkingon,andeverychapterpresentsanin-depthanalysisofthecurrent
methods for modeling Nonlinear Structural Dynamics and Damping.
ThemissionofIFToMMistopromoteresearchanddevelopmentinthefieldof
machines and mechanisms, both theoretically and experimentally, and this book
aimstospreadtheknowledgeandexperienceoftheTC-Vibrationmembers.Thus,
thisbookaimstopresentrelevanttopicsondynamicsandvibrationsthatareofthe
interest of the community and could help in the solution of practical applications.
The chapters of this book also present questions for further research and oppor-
tunity areas for future improvements in modeling and validating our current
understanding of Nonlinear Dynamics.
The chapters are related to the modeling of nonlinear structures and nonlinear
vibrations, presenting techniques for identifying nonlinear responses, the applica-
tion of nonparametric methods for analyzing nonlinear mechanical systems and
structures, and the analysis of synchronization in complex mechanical systems.
Friction and damping are fundamental parameters in the analysis of nonlinear
structures; therefore, this book includes contributions related to the development
and analysis of damping models.
v
vi Preface
Reviewingthetableofcontentswillletyouknowthatthisbookbringstogether
theresultsofresearchtopicsofcurrentinterestthatarefullyexplained.Authorsthat
haveagreatexperienceinthematter,andarewillingtosheartheirknowledgewith
the scientific and engineering community present every chapter.
I want to thank the Publisher and Editorial staff of Springer for helping the
publication of this book.
Querétaro, Mexico Juan Carlos Jauregui
November 2018
Contents
1 Introduction to Scientific Computing Technologies for Global
Analysis of Multidimensional Nonlinear Dynamical Systems . . . . . . 1
Nemanja Andonovski, Franco Moglie and Stefano Lenci
2 Review of Synchronization in Mechanical Systems. . . . . . . . . . . . . . 45
Mihir Sen and Carlos S. López Cajún
3 Research on Vibration Suppression of Nonlinear Energy Sink
Under Dual-Frequency Excitation. . . . . . . . . . . . . . . . . . . . . . . . . . . 71
B. Sun and Z. Q. Wu
4 Identification of Nonlinearities in Mechanical Systems
Using Recurrence Plots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
J. C. Jauregui-Correa
5 Passive Vibration Control Using Viscoelastic Materials . . . . . . . . . . 119
D. A. Rade, J.-F. Deü, D. A. Castello, A. M. G. de Lima
and L. Rouleau
6 Dry-Friction Damping in Vibrating Systems, Theory
and Application to the Bladed Disc Assembly. . . . . . . . . . . . . . . . . . 169
Ludek Pesek, Ladislav Pust, Pavel Snabl, Vitezslav Bula,
Michal Hajzman and Miroslav Byrtus
7 Bifurcation-Based Shimmy Analysis of Landing Gears
Using Flexible Multibody Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
C.J.J.Beckers,A.E.Öngüt,G.Verbeek,R.H.B.Fey,Y.Lemmens
and N. van de Wouw
8 Spectral Analysis of Nonlinear Vibration Effects Produced
by Worn Gears and Damaged Bearing in Electromechanical
Systems: A Condition Monitoring Approach . . . . . . . . . . . . . . . . . . 293
J. J. Saucedo-Dorantes, M. Delgado-Prieto, R. A. Osornio-Rios
and R. J. Romero-Troncoso
vii
Chapter 1
Introduction to Scientific Computing
Technologies for Global Analysis
of Multidimensional Nonlinear
Dynamical Systems
NemanjaAndonovski,FrancoMoglieandStefanoLenci
Abstract To determine global behaviour of a dynamical system, one must find
invariant sets (attractors) and their respective basins of attraction. Since this can-
not be made extensively with analytical methods, the numerical global analysis is
currentlythesubjectofintensiveresearch,especiallyforstronglynonlinear,multi-
dimensionaldynamicalsystems.Numericalanalysisindimensionshigherthanfour
present a challenge, since it requires significant computing resources. Numerical
methods used in global analysis that can benefit from high-power computing are
thosethatcanparallelizeeitherdataortaskelaborationonalargescale.Masspar-
allelization comes with large number of difficulties, restrictions and programming
hazards.Whennotimplementedincompliancewithhardwareorganization,dataand
instructionmanagementcanleadtoseverelossofparallelalgorithmperformance.
Systematicandmethodicalapproachtodesignparallelprogramsis,therefore,critical
togetthemostfromexpensivehigh-powercomputingsystemsandtoavoidunreal-
isticspeed-upexpectation.Consideringthesedifficulties,thegoalofthischapteris
tointroducereaderstotheworldofhigh-powercomputingsystemsforscienceand
global analysis of strongly nonlinear, multidimensional dynamical systems. Topic
covered are classification and performance of hardware and software, classes of
computingproblemsandmethodicaldesignofprograms.Twomajorhardwareplat-
formsusedforscientificcomputing,clustersandsystemswithcomputationalGPU
areconsidered.Functionalityofwidelyutilizedsoftwaresolutions(OpenMP,MPI,
CUDAandOpenCL)forhigh-powercomputingsystemsisdescribed.Performance
ofindividualcomputercomponentsareaddressedsothatthereadercanunderstand
advantages, disadvantages, efficiency and limits of each hardware platform. With
B
N.Andonovski ( )·F.Moglie·S.Lenci
PolytechnicUniversityofMarche,Ancona,Italy
e-mail:[email protected]
F.Moglie
e-mail:[email protected]
S.Lenci
e-mail:[email protected]
©SpringerNatureSwitzerlandAG2019 1
J.C.Jauregui(ed.),NonlinearStructuralDynamicsandDamping,
MechanismsandMachineScience69,
https://doi.org/10.1007/978-3-030-13317-7_1
2 N.Andonovskietal.
this knowledge users can judge if their computation problem is suitable for mass
parallelization.Ifthisisthecase,whichhardwareandsoftwareplatformstouse.To
avoidmanytrapsofparallelprogramming,oneofthemethodicaldesignapproaches
iscovered.Topicisclosedwithexampleapplicationsinscienceandglobalanalysis.
1.1 Introduction
Wellexploredanalyticalmethodsforlinearphenomenaisnotviabletofullydeter-
minedynamicsofsystemsthatmodelreallifeapplication.Lackofanalyticalmethods
haveledtodevelopmentofvariousnumericalmethodsforglobalanalysisofnonlin-
eardynamicalsystems.Numericalmethodsofferpossibilitytosolveproblemsthat
donothave analytical solutioninclosedform,sacrificing generalityofsolution—
any change in system parameters require new computations. To determine global
behaviourofnonlinearsystems,theamountofcomputationsincreasesdramatically
andrequirelargecomputingresources,especiallyinhigherdimensions[1, 2].
Historicalrootsofnumericalcomputationsarefoundinrudimentarymechanical
calculating devices that over long number of years have evolved to contemporary
electricalsupercomputers.Majorpointofcalculatingmachinesremainsthesame—to
aidpeopleinsolvingvarious,mostlymathematical,problems.Precursorsofelectrical
computers are mechanical tools like simple adding devices, abacus, mechanisms
for drawing integrals of graphical functions or mechanical machines that integrate
differentialequations[3].
Transition from various mechanical computers to electrical ones were made
withimplementationofconceptmachinecapabletocomputeanythingthatiscom-
putable (Turing machine). First electrical, vacuum tube computer, EINIAC (Elec-
tronic Numerical Integrator and Calculator), marks beginning of new era that will
leadtocomputationalcapacitythatsurpassesanythingeverimagined.Technology
evolvedtosuchscalethatfunctionalityofmechanicalcalculatingmachinesarerepro-
ducedwithintegratedcircuits,approx.10nminsizeeach[3–5].
High complexity of massively parallel computing systems used in science and
engineeringoftencausedifficultiesduringprogramdesign,particularlyforthosenot
educated in information technologies. In this chapter we aim to introduce readers
to the capabilities of modern day computer systems and systematically explain all
conceptsneededtostartmakingefficientprogramforlarge-scalenumericalcomput-
ingofglobalbehaviourforhigh-dimensionalnonlineardynamicalsystems.Before
tacklingproblemsofhigh-powercomputing,itisnecessarytoanalyseperformance
ofbasiccomputercomponentsfromwhichsupercomputersaremadeof.Organiza-
tionofcomponentsaredescribedthrougharchitecturesthatactaslogicalconcepts
capable to deal with various computational problems. Families of problems that
benefit from mass parallelization are explained along with architectures and com-
puterimplementationsabletoefficientlycomputerelatedtasks.Systematicdesign
methodiscrucialtoavoiddangersofparallelexecutionthatdonotexistinsequential
approach.Firststepistodecidewhichhardwareplatformismostefficientforcom-
