tuned-mass damper design -...
TRANSCRIPT
Tuned-Mass Damper Design A Case Study
Dr. James L. Lamb
AG&E/Structural Engenuity
15280 Addison Rd, Suite 310, Addison, Texas 75001 Office: 214.520.7202
www.age-se-vibe.com
Tuned-Mass Damper Design—Case Study, 2
Topics
What is a Tuned-Mass Damper?
Case Study:
Initial Site Survey—Will a Tuned-Mass Damper Work?
Tuned-Mass Damper Design and Analysis
Prototype Testing
Installation and Performance Verification
Summary
Tuned-Mass Damper Design—Case Study, 3
Tuned-Mass Dampers
m
kf
Spring
TMD
2
1
Mass and Coil Spring Pendulum Mass and Flexure
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gfTMD
2
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mL
EIfTMD 3
48
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• 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 structure’s dominant mode (frequency fMode ≈ fTMD) 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 critical
Probably the least expensive form of TMD; can be tailored for almost any application
Ideal for low-frequency applications like tall buildings or flexible walkways
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L
Tuned-Mass Damper Design—Case Study, 4
Industrial Plant Application
Vibration (Acceleration) Measurements Were Acquired on the Ground at the Base of the Control Room, Along the Supporting Columns, and in the Control Room Itself
The control room sways side-to-side since the plant became operational
The motion persists throughout the day and night
The level of motion is annoying to staff assigned to the control room
Control Room
Site Overview
Tuned-Mass Damper Design—Case Study, 5
Site Survey—Problem Diagnosis (1/2)
Subsequent Data Analysis Identified all Significant Sources of Vibration; The Steel Frame’s Fundamental Sway Mode at 3.5 Hz is of Primary Concern
Motion
Measured vibration data at foundation, along a column, and in the control room
Power Spectrum
Control Room and Structural Frame
Tuned-Mass Damper Design—Case Study, 6
Site Survey—Problem Diagnosis (2/2)
Vibration Near 3.5 Hz is 3 Times Higher than the Human-Comfort Limit; Need to Reduce Vibration by 70%—Tuned-Mass Dampers are a Practical Option
Human Vibration Sensitivity
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
Tuned-Mass Damper Design—Case Study, 7
Structural Dynamics Model of Existing Building
Finite Element Model Control Room Mass
(both sides)
12 ft
28 ft
24 ft
18 ft
Structural member properties taken from existing-structure drawings
Mass of cables and pipes (not shown in model) at each level estimated from photographs
Mass of prefabricated control room (not shown) obtained from manufacturer; additional mass of fit-out estimated
Structural Dynamics Model Confirms Sway Mode at 3.5 Hz; Only 3 Bays Modeled Because They Act Independently in East/West Direction
Tuned-Mass Damper Design—Case Study, 8
Model Validation via Frequency Response
Frame Sway Mode (3.5 Hz) Frequency Response
3.5 Hz
Structural Dynamics Model Parameters Adjusted to Match Measured Sway Mode at 3.5 Hz—The Model can Now be Used to Design the Tuned-Mass Dampers
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
)|
Tuned-Mass Damper Design—Case Study, 9
TMD Conceptual Design
Simple Design of Flexure-Based TMD Minimizes the Fabrication Cost; TMD Performance is Verified During Prototype Testing Prior to Installation
Damping in joint
Flexure Bars
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
Tuned-Mass Damper Design—Case Study, 10
Optimum TMD Performance
Reinforcement TMD and bldg move in phase
Cancellation TMD opposes bldg motion
Damping TMD and bldg 90° out of phase
Reduction in Vibration (Increases with TMD mass)
TMD Mass
TMD Mass
Bldg Bldg
Original Bldg
Bldg with TMD
TMD has no effect at frequencies below or above the “tuning” frequency
Analysis Indicates that the TMDs Reduce the Vibration by 90% at 3.5 Hz; However, a Realistic Performance Assessment Must Consider Excitation Near 3.5 Hz
In-Phase Mode Out-of-Phase Mode
|H(f
)|
Tuned-Mass Damper Design—Case Study, 11
TMD Internal Damping Optimization
Maximum Reduction
Original bldg
Out-of-phase mode In-phase mode
There is an “Optimal” Level of Internal Damping, but 8% to 16% Critical Damping Usually Yields a Robust Range for Very Good Overall Vibration Mitigation
Frequency Response: Effect of TMD Damping If TMD damping is too low, both peaks 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 two modes merge into a single peak and slightly worse performance
TMDs made of steel or alum-inum usually require additional damping
|H(f
)|
Tuned-Mass Damper Design—Case Study, 12
Vibration Mitigation Effectiveness = TMD Mass
Select TMD Mass (i.e. TMD Cost) to Achieve Desired Mitigation Over Narrow Band; Need to Reduce Vibration by at Least 70%, so Use 1500 lbm/TMD
Results for optimized damping for each TMD mass:
190 lbm 47% reduction 375 lbm 55% reduction 750 lbm 63% reduction 1500 lbm 71% reduction 3000 lbm 78% reduction
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
Tuned-Mass Damper Design—Case Study, 13
Prototype TMD Testing 45-in Long Flexure
41-in Long Flexure
Constrained-Layer Damping
SBR Rubber Layers and a Flexure Bar Length of 37.5 inches Identified as Best Combination and Provides About 12% Damping—Satisfies Design Requirement
Various combinations of the TMD flexure bar length and constrained-layer damping material were tested to find the best combination
M = 1500 lbm
31-in Long Flexure
Tuned-Mass Damper Design—Case Study, 14
Installation and Performance Assessment
Tuned-Mass Dampers Successfully Reduce the Vibration in the Control Room Below 0.005-g Limit as Predicted; Staff Report Environment is Significantly Improved
TMDs Installed on Structure Before/After Vibration
The TMDs were tested after installation to verify the tuning. Data were also acquired in the control room for comparison with the original motion
Tuned-Mass Damper Design—Case Study, 15
Summary
The tuned-mass damper is a viable vibration mitigation solution when the motion is caused by a low-damped mode of the structure
Tuned-mass dampers can be fabricated in many different forms based on the physical and aesthetic constraints
Design process for tuned-mass dampers:
Site Survey: Measure the frequency and magnitude of the motion
Analyze/Design: Develop a model of the existing structure and determine the TMD mass and placement of TMD(s) to achieve the desired vibration mitigation
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 confirm their performance and that the mitigation objective was achieved
Expect 70% to 80% reduction in the vibration after installation of the tuned-mass dampers