Exploring the concept of Tuned Mass Damper

1. Solving the problem of
LAX THEME BUILDING
‘Tuned Mass Damper’
Viranpat Jiratipayabood L2C (Orange)

2. LAX THEME BUILDING
http://traveltips.usatoday.com/DM-Resize/photos.demandstudios.
com/getty/article/83/101/86518223_XS.jpg?w=560&h=560&keep_ratio=1&webp=1

3. Problems
● In 2007 : 1,000 lb of plaster separated from the arches of the building.
● The building is considered a cultural and historical monument.
● Did not meet the updated seismic safety standards
● Would NOT survive a strong earthquake
Solutions
● Install the typical Tuned Mass Damper (TMD) at the base of the building
○ BUT: this would alter the design of the building/not conserve the iconic
structure and value.
● Install the TMD to the top core of the building
○ YES!
○ No alteration in the building’s design
○ Minimizes the cost (as the building does not need to be expanded or
reconstructed

4. PRINCIPLE of TMD
● TMD would counter and stabilize movement of the building
● 3 basic elements: mass, stiffness and damping
○ Mass/stiffness: selected in order to provide TMD resonance frequency
that is close to that of the structure
○ Damping: selected to optimize energy dissipation
View animation:
http://commons.wikimedia.
org/wiki/File%
3ATuned_mass_damper.gif

5. http://i.ytimg.
com/vi/sl5_GWjzTCE/maxresdefault.jpg
FREE BODY DIAGRAM:
Force of damper is opposite
to force of motion
TMD can be compared to the Spring
Damper
b = damper
k = spring (only is
M = mass

6. CONCEPT OF TMD
● Stabilizes movement caused by harmonic vibration
● When frequency of the building is excited
○ Damper will counter the vibration
○ Energy is dissipated by damper inertia force
● Forces of damper:
○ transform parts of oscillator’s kinetic energy into thermal energy
(decreasing the amplitude of oscillation)
○ energy then eventually turns into thermal energy and oscillation stops.

7. HOW?
● The most important concept is to have TMD’s frequency similar to that of
the building.
❖ GIVEN: and that
■ The period of TMD can be figured out in order to tune the
frequency
■ Through adjusting the length of the pendulum, or in the Theme
building’s case, the height of the metal plate (mass), the
frequency of the TMD can be tuned into that of the building’s.

8. Critically Damped Oscillator
● The TMD concept can also be understood through the concept of Critically
damped oscillator :
● ω₀= b/2m
○ b = damping constant
○ m = mass
○ ω₀ = oscillation frequency when b = 0
● As b increases → frequency of damped oscillator decreases → taking
more time to complete an oscillation.
● This means the oscillator to reach equilibrium (return to normal position)
without overcoming the damping constant (b).