Transcription
Chapter 13Tuned-Mass trolChapterChapter13 – Tuned-Mass1 - IntroductionDampers1
CONTENT1.2.3.4.5.6.7.8.IntroductionTheory of Undamped Tuned-mass Dampers Under HarmonicLoadingTheory of Undamped Tuned-mass Dampers Under HarmonicBase MotionTheory of Damped Tuned-mass Dampers Under HarmonicLoadingSeismic Application of Tuned-Mass DampersAnalysis of Structures with Tuned-Mass DampersSeismic Response of Inelastic Buildings with Tuned-MassDampersDesign trolControlChapterChapter13 – Tuned-Mass1 - IntroductionDampers2
Major References Chapter 8– Sections 8.1 to ChapterChapter13 – Tuned-Mass1 - IntroductionDampers3
1. Introduction Tuned-mass dampers (TMDs) or vibration absorbers:– First suggested by Hermann Frahm in 1909 (US Patent #989958).– Relatively small mass-spring-dashpot systems calibrated to be inresonance with a particular mode of vibration.– Usually installed on roofs of buildings. TMDs effective in reducing wind-induced vibrations in high-risebuildings and floor vibrations induced by occupant activity. More recently, TMDs considered for seismic protection of ControlChapterChapter13 – Tuned-Mass1 - IntroductionDampers4
1. Introduction Advantages of TMDs:– Capable of significantly reducing dynamic response of linearstructures.– Construction is simple: assembly of a mass, a spring, and a viscousdamper at a given point on the structure.– No need for external power source or sophisticated hardware. Disadvantages of TMDs:– Require a relatively large mass.– Require large space for installation.– Usually undergo large relative displacements and require largeclearances.– Need to be mounted on a smooth surface to minimize friction andfacilitate free motion. Basic theory of TMDs presented. Potential seismic applications of TMDs ontrolChapterChapter13 – Tuned-Mass1 - IntroductionDampers5
1. Introduction 373-ton TMD in Citycorp Center, New York City––––––First lateral natural frequency 0.16 Hz.1% damping ratio in first mode.TMD installed on 63rd floor.TMD produces effective damping ratio of 4%.Wind induced accelerations reduced by 50%.Linear nitrogen charged springs, hydrostatic bearings, control actuators,power supply and electronic ntrolChapterChapter13 – Tuned-Mass1 - IntroductionDampers6
1. Introduction 2-300-ton TMDs in John Hancock Tower, Boston– In-phase motions control lateral response.– Out-of-phase motions control torsional ontrolChapterChapter13 – Tuned-Mass1 - IntroductionDampers7
1. olControlChapterChapter13 – Tuned-Mass1 - IntroductionDampers8
1. Introduction 660-ton Pendulum TMD to reduce windvibrations in 101 Taipei Building, trolChapterChapter13 – Tuned-Mass1 - IntroductionDampers9
1. Introduction 5-ton Pendulum TMD to reduce wind vibrations ofMarina Bay SkyPark in ControlChapterChapter13 – Tuned-Mass1 - IntroductionDampers10
1. Introduction Seismic upgrade of LAX Airport ThemeBuilding with 600-ton TMD and ntrolControlChapterChapter13 – Tuned-Mass1 - IntroductionDampers11
2. Theory of Undamped Tuned-massDampers Under Harmonic trolChapterChapter13 – Tuned-Mass1 - IntroductionDampers12
2. Theory of Undamped Tuned-massDampers Under Harmonic trolChapterChapter13 – Tuned-Mass1 - IntroductionDampers13
2. Theory of Undamped Tuned-massDampers Under Harmonic trolChapterChapter13 – Tuned-Mass1 - IntroductionDampers14
2. Theory of Undamped Tuned-massDampers Under Harmonic trolChapterChapter13 – Tuned-Mass1 - IntroductionDampers15
2. Theory of Undamped Tuned-massDampers Under Harmonic trolChapterChapter13 – Tuned-Mass1 - IntroductionDampers16
2. Theory of Undamped Tuned-massDampers Under Harmonic trolChapterChapter13 – Tuned-Mass1 - IntroductionDampers17
2. Theory of Undamped Tuned-massDampers Under Harmonic trolChapterChapter13 – Tuned-Mass1 - IntroductionDampers18
2. Theory of Undamped Tuned-massDampers Under Harmonic trolChapterChapter13 – Tuned-Mass1 - IntroductionDampers19
2. Theory of Undamped Tuned-massDampers Under Harmonic trolChapterChapter13 – Tuned-Mass1 - IntroductionDampers20
2. Theory of Undamped Tuned-massDampers Under Harmonic trolChapterChapter13 – Tuned-Mass1 - IntroductionDampers21
2. Theory of Undamped Tuned-massDampers Under Harmonic trolChapterChapter13 – Tuned-Mass1 - IntroductionDampers22
3. Theory of Undamped Tuned-massDampers Under Harmonic Base rolChapterChapter13 – Tuned-Mass1 - IntroductionDampers23
3. Theory of Undamped Tuned-massDampers Under Harmonic Base rolChapterChapter13 – Tuned-Mass1 - IntroductionDampers24
3. Theory of Undamped Tuned-massDampers Under Harmonic Base rolChapterChapter13 – Tuned-Mass1 - IntroductionDampers25
3. Theory of Undamped Tuned-massDampers Under Harmonic Base rolChapterChapter13 – Tuned-Mass1 - IntroductionDampers26
3. Theory of Undamped Tuned-massDampers Under Harmonic Base rolChapterChapter13 – Tuned-Mass1 - IntroductionDampers27
3. Theory of Undamped Tuned-massDampers Under Harmonic Base rolChapterChapter13 – Tuned-Mass1 - IntroductionDampers28
4. Theory of Damped Tuned-massDampers Under Harmonic trolChapterChapter13 – Tuned-Mass1 - IntroductionDampers29
4. Theory of Damped Tuned-massDampers Under Harmonic trolChapterChapter13 – Tuned-Mass1 - IntroductionDampers30
4. Theory of Damped Tuned-massDampers Under Harmonic ontrolChapterChapter13 – Tuned-Mass1 - IntroductionDampers31
4. Theory of Damped Tuned-massDampers Under Harmonic Loadinga1 pterChapter13 – Tuned-Mass1 - IntroductionDampers32
4. Theory of Damped Tuned-massDampers Under Harmonic trolChapterChapter13 – Tuned-Mass1 - IntroductionDampers33
4. Theory of Damped Tuned-massDampers Under Harmonic trolChapterChapter13 – Tuned-Mass1 - IntroductionDampers34
4. Theory of Damped Tuned-massDampers Under Harmonic trolChapterChapter13 – Tuned-Mass1 - IntroductionDampers35
4. Theory of Damped Tuned-massDampers Under Harmonic ntrolChapterChapter13 – Tuned-Mass1 - IntroductionDampers36
4. Theory of Damped Tuned-massDampers Under Harmonic trolChapterChapter13 – Tuned-Mass1 - IntroductionDampers37
4. Theory of Damped Tuned-massDampers Under Harmonic trolChapterChapter13 – Tuned-Mass1 - IntroductionDampers38
4. Theory of Damped Tuned-massDampers Under Harmonic trolChapterChapter13 – Tuned-Mass1 - IntroductionDampers39
4. Theory of Damped Tuned-massDampers Under Harmonic trolChapterChapter13 – Tuned-Mass1 - IntroductionDampers40
5. Seismic Application of Tuned-Mass trolChapterChapter13 – Tuned-Mass1 - IntroductionDampers41
5. Seismic Application of Tuned-Mass trolChapterChapter13 – Tuned-Mass1 - IntroductionDampers42
5. Seismic Application of Tuned-Mass trolChapterChapter13 – Tuned-Mass1 - IntroductionDampers43
6. Analysis of Structures withTuned-Mass Dampers TMD tuned to a single structural frequency. For seismic applications, TMDs usually tuned tofundamental mode of vibration. TMD often installed on building olChapterChapter13 – Tuned-Mass1 - IntroductionDampers44
6. Analysis of Structures withTuned-Mass trolChapterChapter13 – Tuned-Mass1 - IntroductionDampers45
6. Analysis of Structures withTuned-Mass trolChapterChapter13 – Tuned-Mass1 - IntroductionDampers46
6. Analysis of Structures withTuned-Mass trolChapterChapter13 – Tuned-Mass1 - IntroductionDampersx1 xNx2 xN z47
6. Analysis of Structures withTuned-Mass Dampers Same approach can mitigate vibrations of any mode. A structure with a TMD may experience inelasticdeformations during a strong earthquake. When inelastic deformations occur, fundamentalfrequency decreases. TMD may lose effectiveness due to de-tuning effect. Detuning phenomenon discussed in next ntrolChapterChapter13 – Tuned-Mass1 - IntroductionDampers48
7. Seismic Response of InelasticBuildings with Tuned-Mass Dampers Carr (2005) investigated seismic response ofshear wall reinforced concrete buildingsequipped with TMDs Main objective to investigate seismic fragilityof elastic and inelastic reinforced concretebuildings with TMDs of various sizes Ensembles of ground motions representingvarious seismic hazard rolChapterChapter13 – Tuned-Mass1 - IntroductionDampers49
7. Seismic Response of InelasticBuildings with Tuned-Mass Dampers Building Models– Shear wall-type buildings, 3 and 10, and 25 ntrolChapterChapter13 – Tuned-Mass1 - IntroductionDampers50
7. Seismic Response of InelasticBuildings with Tuned-Mass Dampers Analysis Procedure– Two-dimensional lumped-mass model of each building model with and withoutTMDs.– Torsional effects neglected.– Each model included only one wall with one gravity column.– Total dead loads acting on interior columns applied to gravity column.– TMD modeled as a SDOF system on roof of building.– TMD tuned to Equations (8.43) and trolChapterChapter13 – Tuned-Mass1 - IntroductionDampers51
7. Seismic Response of InelasticBuildings with Tuned-Mass Dampers Ground Motions– Ensembles of synthetic strong ground motions generatedfor Southern California site.– Ground motions for 2%, 5%, 10%, and 20% probabilitiesof exceedence in 50 years (return periods of 2475, 975,475, and 224 years).– Each ensemble comprised of 25 earthquake records.– Total of 100 strong ground motions considered.– Strong motions simulated using the Specific Barrier Model(Papageorgiou and Aki 1983a, trolChapterChapter13 – Tuned-Mass1 - IntroductionDampers52
7. Seismic Response of InelasticBuildings with Tuned-Mass trolChapterChapter13 – Tuned-Mass1 - IntroductionDampers53
8. Design trolControlChapterChapter13 – Tuned-Mass1 - IntroductionDampers54
8. Design Considerationse.g.:ζeq 0.20ζ1 0.05µ 0.41 very ontrolChapterChapter13 – Tuned-Mass1 - IntroductionDampers55
Thank lChapterChapter13 – Tuned-Mass1 - IntroductionDampers56
damper at a given point on the structure. – No need for external power source or sophisticated hardware. Disadvantages of TMDs: – Require a relatively large mass. – Require large space for installation. – Usually undergo large relative displacements and require large clearances.
