tuned-mass damper design-a case study
TRANSCRIPT
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Tuned-Mass Damper DesignA Case Study
Dr. James (Jay) Lamb
Structural Engenuity, Inc.
(972) 247-9250 x212
http://www.structuralengenuity.com/http://www.structuralengenuity.com/ -
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Agenda
What is a Tuned-Mass Damper?
Case Study: TETRA Technologies Project
Initial Site SurveyWill a Tuned-Mass Damper Work?
Tuned-Mass Damper Design and Analysis
Prototype Testing
Installation and Performance Verification
Summary and Conclusions
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Tuned-Mass Dampers
m
kf
Spring
TMD
2
1
Mass and Coil Spring PendulumMass and Flexure
L
g
fTMD2
1
mL
EIfTMD 3
48
2
1
A tuned-mass damper is a mass-spring-damper system that is attached to a structure
to reduce the amplitude of undesirable motion
The mass, spring stiffness, and damping factor must be tuned relative to the existing
structures dominant mode (frequencyfModefTMD) responsible for the motion
The location on the structure where the TMD(s) is/are attached is critical
TMDs can have many different forms depending upon the application:
A very compact form of TMD; ideal
for space-limited applications or
when concealment is criticalProbably the least expensive form of
TMD; can be tailored for almost any
application
Ideal for low-frequency
applications like tall
buildings or flexiblewalkways
L
L
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TETRA Technologies CaCl2 Plant
SEI Asked to Perform a Site Vibration Survey, Identify the Cause of
the Problem, and Provide Recommendations for Possible Solutions
Control room swayed side-
to-side immediately when
plant opened
Motion persists throughout
the day and night
Staff irritated by level ofmotion and complained to
management
Original engineers tried and
failed to solve the problem
Control Room
Site Overview
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Site SurveyProblem Diagnosis (1/2)
SEI Measured and Identified all Significant Sources of Vibration;
The 3.5-Hz Motion is the Primary Source of the Staffs Discomfort
Motion
Measured vibration data at foundation,
along a column, and in the control room
Power Spectrum
Control Room and Structural Frame
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Site SurveyProblem Diagnosis (2/2)
Vibration Near 3.5 Hz is 3 Times Higher than the Human-Comfort Limit;
Ground-Borne Vibration Excites the Sway Mode of Structural Frame
Need to Reduce Vibration by 70%Tuned-Mass Damper is Practical Solution
Human Perception Criteria
Front-to-Back
Criteria
0.005-g
Limit
Measured Control Room Vibration (3.5 Hz)
Limit = 0.005 g
Data filtered around 3.5 Hz
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Structural Dynamics Model of Existing Building
Finite Element ModelControl Room Mass
(both sides)
12 ft
28 ft
24 ft
18 ft
Structural member properties taken fromexisting-structure drawings
Mass of cables and pipes (not shown) at each
level estimated from photographs
Mass of prefabricated control room (not shown)
obtained from manufacturer; additional mass of
fit-out estimated
Structural Model has Same Stiffness and Mass Properties as Existing Structure;
Only 3 Bays Modeled Because They Act Independently in East/West Direction
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Model Validation via Frequency Response
Frame Sway Mode (3.5 Hz) Frequency Response
3.5 Hz
Model Parameters Adjusted so Models Sway Mode Matches the Measured
Motion of 3.5 HzModel can now be Used to Design/Assess TMDs
Motion at top (control
room) is magnified by
factor of 85 relative to
motion of foundation
Ratio of control room motion
to foundation motion
|H(f)|
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TMD Conceptual Design
Simple Design of Flexure-Based TMD Minimizes Cost and Performance
can be Verified During Prototype Testing Before Final Installation
Damping
in joint
FlexureBars
Mass
Attach to
Existing Bldg
Flexure-type (cantilever) TMD is
appropriate for this structure
Constrained-layer damping is
incorporated into joint
Flexure bars must be stiffer to
compensate for joint flexibility
East/West flexural mode (fTMD)required to be 3.4 Hz ( 3.5 Hz)
Place 3 TMDs on the columns
supporting the control room
Idealized
Model
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Optimum TMD Performance
ReinforcementTMD and Bldg
Move in Phase
CancellationTMD Opposes Bldg
Motion
DampingTMD and Bldg
90 Out of Phase
Reduction in Vibration(Increases With TMD Mass)
TMD
Mass
TMD
Mass
BldgBldg
Original Bldg
Bldg with TMD
TMD Has No Effect at Frequencies Belowor Above the Tuning Frequency
Analysis Indicates TMDs Reduce Vibration by 90% of Initial
Level Near 3.5 HzReal Performance will not be this Good
In-Phase Mode Out-of-Phase Mode
|H(f)|
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TMD Internal Damping Optimization
Maximum
Reduction
Original Bldg
Out-of-phase modeIn-phase mode
There is an Optimal Level of Internal Damping, but 8% to 16% Critical
Damping Usually Yields a Robust Range for Very Good Performance
Frequency Response: Effect of TMD Damping
If TMD damping is too low, bothpeaks for the in-phase and out-
of-phase modes will be present
Optimal damping produces a
nearly flat curve
If damping is too high, the twomodes merge into a single peak
TMDs made of steel or alum-
inum usually require additional
damping be incorporated
|H(f)|
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Vibration Mitigation Effectiveness = TMD Mass
Select TMD Mass to Achieve Desired Mitigation Over Narrow Band (1 Hz)
Need to Reduce Vibration by at Least 70% HereUse 1500 lbm/TMD
Results for optimized dampingfor each TMD mass
Results (1-Hz Bandwidth):190 lbm 47% reduction
375 lbm 55% reduction
750 lbm 63% reduction
1500 lbm 71% reduction3000 lbm 78% reduction
Selection of bandwidth is
somewhat arbitrary
Increment of improvement in
vibration mitigation diminishes
with increasing mass
Frequency Response: Effect of TMD Mass
Determine vibration
reduction over band for
broadband excitation
High
Low
High
Low
f
f
f
fm
dffH
dffHR
2
0
2
)(
)(1
|H(f)|
fLow fHigh
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Prototype TMD Testing45-in Long Flexure
41-in Long Flexure
31-in Long Flexure
Constrained-Layer
Damping
SBR Rubber Layers and a Flexure Bar of 37.5 inches Identified
as Best Combination and Provides About 12% Damping
SEI Tested Various Combinations of TMD Flexure Bar Lengths and
Constrained-Layer Damping Materials to Find Best Combination
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Installation and Performance Assessment
Tuned-Mass Dampers Successfully Reduce the Vibration in the Control Room
Below 0.005-g Limit; Staff Report Environment is Significantly Better Now
TMDs Installed on Structure Before/After Vibration
SEI tested the TMDs after installation to verify the tuning. Data were also
acquired in the control room for comparison with the original motion
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Summary and Conclusions
Tuned-mass dampers can be fabricated in many different forms
based on the physical and aesthetic constraints of the application
Tuned-mass dampers are viable vibration mitigation solutions whenthe motion is caused by a low-damped mode of the structure
Design process for tuned-mass dampers
Site Survey: Measure the frequency and magnitude of the undesirable motion
Analyze/Design: Develop model of existing structure and determine the TMDmass and placement of TMD(s) to achieve vibration mitigation requirement
Test: Perform prototype testing of the TMD to fine-tune the design
Install/Verify: Measure the motion of the TMD(s) on the structure to confirmperformance and that the mitigation objective was achieved
Expect 70% to 80% reduction in the vibration after installation
Weight of TMD is typically about 5% to 10% of effective weight ofmode responsible for the motion
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Questions? Contact SEI
Please contact us with any vibration mitigation issues you
have and let us help you to resolve them
Structural Engenuity, Inc.
Dr. James (Jay) L. Lamb
Office: (972) 247-9250
Cell: (214) 412-8388
www.structuralengenuity.com
mailto:[email protected]:[email protected]