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

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Spring

TMD

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Mass and Coil Spring Pendulum Mass and Flexure

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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

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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