Vibration Control of Large Scale Flexible Structures Using Magnetorheological Dampers Approved

216 Pages·2012·5.98 MB·English

Vibration Control of Large Scale Flexible Structures Using
Magnetorheological Dampers
by
Wei Liu
ADissertation
Submittedto theFaculty
of the
WORCESTER POLYTECHNIC INSTITUTE
In partial ful(cid:2)llmentofthe requirementsforthe
DegreeofDoctorof Philosophy
in
MechanicalEngineering
March2,2005
Approved:
ProfessorZhikun Hou,MajorAdvisor
ProfessorMichaelA.Demetriou,Co-advisor
ProfessorJohn Sullivan,CommitteeMember
ProfessorJamesHu, CommitteeMember
(University ofRhode Island)
ProfessorMarkRichman,GraduateCommittee Representative
Copyright ' 2005 by Wei Liu
ALL RIGHTS RESERVED
Use or inclusion of any portion of this document in another work intended for
commercial use will require permission from the copyright owner.
Abstract
Structural vibration control (SVC) of large scale structures using the magnetorheological
(MR) dampers are studied. Some key issues, i.e. model reduction, suppression of spillover
instability, optimal placement of actuators and sensors, modeling of the MR dampers and their
applications inSVC system forlargescalestructures,areaddressed inthis work.
A new model reduction method minimizing the error of a modal-truncation based reduced
order model(ROM) is developed. The proposed method is implementedby using a GeneticAl-
gorithm(GA),andcanbeef(cid:2)cientlyusedto(cid:2)ndaROMforalargescalestructure. Theobtained
ROM has a (cid:2)nite normand therefore can be used for controllerdesign. The mechanism
2 2
H H
of the spillover instability is studied, and a methodology to suppress the spillover instability in
a SVC system is proposed. The suggested method uses pointwise actuators and sensors to con-
structa controllerlyinginanorthogonalspacespannedby theseveralselectedresidual modes,
suchthatthespilloverinstabilitycausedbytheseresidualmodescanbesuccessfullysuppressed.
AGAbasednumericalschemeusedto(cid:2)ndtheoptimallocationsforthesensorsandactuatorsof
a SVCsystem is developed. The spatial normis usedas the optimization index. Becausethe
2
H
spatial norm is a comprehensive index in evaluating the dynamics of a distributed system,
2
H
a SVC system using the sensors and actuators located on the obtained optimal locations is able
to achieve a better performance de(cid:2)ned on a distributed domain. An improved model of MR
dampers is suggested such that the model can maintain the desired hysteresis behavior when
noisy data are used. For the simulation purpose, a numerical iteration technique is developed
to solve the nonlineardifferential equations aroused from a passive controlof a structureusing
the MR dampers. The proposed method can be used to simulate the response of a large scale
structuralsystemwiththeMRdampers. Themethodsdevelopedinthis workare(cid:2)nallyveri(cid:2)ed
usinganindustrial roofstructure. Apassiveandsemi-activeSVCsystems aredesignedto atten-
uate the wind-induced structural vibration inside a critical area on the roof. The performances
of the both SVC systems are analyzed and compared. Simulation results show that the SVC
systems using the MR dampers have great potentials in reducing the structural vibration of the
roofstructure.
In Memory of My Grandmothers
To My BelovedSon
Acknowledgments
I am grateful to all people who have contributed towards shaping this disserta-
tion. First of all, I would like to express my sincere gratitude to my advisor, professor
Zhikun Hou, for his comprehensive guidance and continuous support. His obser-
vations and invaluable advice helped me to establish the overall direction of the re-
search and to move forward smoothly. Withtout his support, this work would never
be possible. Financial support from the FM Globalr Research Center is gratefully
acknowledged.
Iwouldlike toexpressmy sincere appreciationtomy co-advisor, professor Michael
A. Demetriou, for his guidance and assistance in helping me to gain a better under-
standing in the control theories. His encouragement and advice have substantially
helped me out in learning this new discipline.
Gratitude goes to my dissertation committee members, professor Sullivan, profes-
sor Richman and professor Hu. Whenever I felt a dead-end in my research, they were
there to give me helping hands. I am thankful to professor Sullivan for teaching me
both theories and practical techniques in numerical analysis from which my research
bene(cid:2)ted. I am thankful to professor Richman for teaching me elasticity theories
and agreeing to provide me a TA assistantship during the end of my research. I am
indebted to professor Hu for his instructive advice on this work.
Thanks also go to professor Dimentberg who gave me valuable help on random
and nonlinear vibration. I would like to express my gratitude towards my colleague
Adriana for all the enlightening discussions with her. I’d like to thank Edyta for her
efforts in keeping our of(cid:2)ce a clean, comfortable place to work. I also wish to express
my appreciation to secretaries of the ME of(cid:2)ce, Barbara Edilberti, Barbara Furhman,
Janice and Pam for all of their assist and cooperation.
I would like to thank my grandfather, my parents, my sister and her husband for
their sustained supports. I shall be more obliged to all of them than I can express.
Finally, Iowespecialthanktomy wife,YiqunHu,forallwhatshedidinsupporting
me in (cid:2)nishing this work. Without her understanding and supports, I would not have
made it this far. My lovely son was brought into this world during the writing of my
dissertation. His arrival added a lot of joy to my tedious work. As a father, I should
have spent more time with him. For this, I felt obliged to him. I therefore dedicate
this dissertation to my son, Andrew.
Wei Liu
Worcester, Massachusetts
CONTENTS
List of Tables v
List of Figures vi
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Overview ofStructuralVibration Control . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Literature Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3.1 ModelReduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3.2 Suppressionof SpilloverInstability . . . . . . . . . . . . . . . . . . . . . . 10
1.3.3 Optimal Locations of Sensorsand Actuators . . . . . . . . . . . . . . . . . 11
1.3.4 ModelingandControlof MRDamper . . . . . . . . . . . . . . . . . . . . 13
1.4 Objectives of theDissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.5 Overview ofthe Dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2 Modeling of FlexibleStructuresand Controller Design 19
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 Mindlin PlateTheory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3 Finite elementFormulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4 ControllerDesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
i
2.4.1 State SpaceForm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.4.2 LQG Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.4.3 Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2
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2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3 Model Reduction 37
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.2 BalancedRealizationand ModelReduction. . . . . . . . . . . . . . . . . . . . . . 38
3.2.1 Controllerabilityand Observability . . . . . . . . . . . . . . . . . . . . . . 38
3.2.2 BalancedRealization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2.3 ModelReductionby BalancedTruncation . . . . . . . . . . . . . . . . . . 41
3.3 Modal Truncation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3.1 TruncationError . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.3.2 ParametricStudy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.4 ModelReductionby Modi(cid:2)ed ModalTruncation . . . . . . . . . . . . . . . . . . . 55
3.4.1 Approximation ofRealSystem. . . . . . . . . . . . . . . . . . . . . . . . . 57
3.4.2 Algorithmof Modi(cid:2)ed ModalTruncationUsingGA Method . . . . . . . . 58
3.5 NumericalExample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4 Suppressionof SpilloverInstability 68
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.2 Mechanismof Spillover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.3 A NullSpaceApproachforSuppressingSpilloverInstability . . . . . . . . . . . . 72
4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.5 NumericalExample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5 Optimal Locations of Sensors/Actuators 90
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.2 Spatial Norm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
2
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ii
5.3 Dominant ModesandReducedOrderModel . . . . . . . . . . . . . . . . . . . . . 94
5.4 GA Method fortheOLSA Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.5 NumericalExample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6 Modeling of MR Dampers and Applications 111
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.2 ModelingofMRFluids Damper . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
6.2.1 Binham Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.2.2 Extended BinghamModel . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.2.3 Bouc-WenModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
6.2.4 Modi(cid:2)ed Bouc-WenModel . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6.2.5 Improvementof theNumericalProperty . . . . . . . . . . . . . . . . . . . 118
6.3 StructuralVibration ControlUsingMRDampers . . . . . . . . . . . . . . . . . . . 120
6.3.1 Passive Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
6.3.2 Semi-ActiveControl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
6.4 NumericalExample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
6.4.1 Passive Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.4.2 Semi-ActiveControl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
7 Vibration Control of a Roof Structure 132
7.1 DynamicResponseAnalysis of RoofStructure . . . . . . . . . . . . . . . . . . . . 133
7.1.1 Wind Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
7.1.2 Responseofthe Roofto the Wind Excitation . . . . . . . . . . . . . . . . . 140
7.2 Modal Analysisof theRoofStructure . . . . . . . . . . . . . . . . . . . . . . . . . 145
7.3 Modelingofthe RoofStructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
7.3.1 Admissible Actuator/SensorLocations . . . . . . . . . . . . . . . . . . . . 147
7.3.2 Optimal Locations of Actuatorsand Sensors . . . . . . . . . . . . . . . . . 149
7.3.3 ReducedOrderModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
7.4 Passive ControlUsing MRDamper . . . . . . . . . . . . . . . . . . . . . . . . . . 155
iii
7.5 Semi-ActivecontrolUsing MRDamper . . . . . . . . . . . . . . . . . . . . . . . . 162
7.6 Less Constrained RoofStructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
7.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
8 Concluding Remarks 175
8.1 Summaryof theWork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
8.2 Main Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
8.3 RecommendationsforFutureWork . . . . . . . . . . . . . . . . . . . . . . . . . . 180
A Newmark Direct Integration Algorithm 182
B EigensystemRealization Algorithm 185
C GeneticAlgorithm 188
Bibliography 193
iv