# Tuned mass damper

A tuned mass damper (TMD), also known as a harmonic absorber or seismic damper, is a device mounted in structures to reduce mechanical vibrations, consisting of a mass mounted on one or more damped springs. Its oscillation frequency is tuned to be similar to the resonant frequency of the object it is mounted to, and reduces the object's maximum amplitude while weighing much less than it.

Tuned mass damper atop Taipei 101
Shanghai Tower tuned mass damper

TMDs can prevent discomfort, damage, or outright structural failure. They are frequently used in power transmission, automobiles and buildings.

## Principle

A schematic of a simple spring–mass–damper system used to demonstrate the tuned mass damper system

Tuned mass dampers stabilize against violent motion caused by harmonic vibration. They use a comparatively lightweight component to reduce the vibration of a system so that its worst-case vibrations are less intense. Roughly speaking, practical systems are tuned to either move the main mode away from a troubling excitation frequency, or to add damping to a resonance that is difficult or expensive to damp directly. An example of the latter is a crankshaft torsional damper. Mass dampers are frequently implemented with a frictional or hydraulic component that turns mechanical kinetic energy into heat, like an automotive shock absorber.

Given a motor with mass m1 attached via motor mounts to the ground, the motor vibrates as it operates and the soft motor mounts act as a parallel spring and damper, k1 and c1. The force on the motor mounts is F0. In order to reduce the maximum force on the motor mounts as the motor operates over a range of speeds, a smaller mass, m2, is connected to m1 by a spring and a damper, k2 and c2. F1 is the effective force on the motor due to its operation.

Response of the system excited by one unit of force, with (red) and without (blue) the 10% tuned mass. The peak response is reduced from 9 units down to 5.5 units. While the maximum response force is reduced, there are some operating frequencies for which the response force is increased.

The graph shows the effect of a tuned mass damper on a simple spring–mass–damper system, excited by vibrations with an amplitude of one unit of force applied to the main mass, m1. An important measure of performance is the ratio of the force on the motor mounts to the force vibrating the motor, F0/F1. This assumes that the system is linear, so if the force on the motor were to double, so would the force on the motor mounts. The blue line represents the baseline system, with a maximum response of 9 units of force at around 9 units of frequency. The red line shows the effect of adding a tuned mass of 10% of the baseline mass. It has a maximum response of 5.5, at a frequency of 7. As a side effect, it also has a second normal mode and will vibrate somewhat more than the baseline system at frequencies below about 6 and above about 10.

The heights of the two peaks can be adjusted by changing the stiffness of the spring in the tuned mass damper. Changing the damping also changes the height of the peaks, in a complex fashion. The split between the two peaks can be changed by altering the mass of the damper (m2).

A Bode plot of displacements in the system with (red) and without (blue) the 10% tuned mass.

The Bode plot is more complex, showing the phase and magnitude of the motion of each mass, for the two cases, relative to F1.

In the plots at right, the black line shows the baseline response (m2 = 0). Now considering m2 = m1/10, the blue line shows the motion of the damping mass and the red line shows the motion of the primary mass. The amplitude plot shows that at low frequencies, the damping mass resonates much more than the primary mass. The phase plot shows that at low frequencies, the two masses are in phase. As the frequency increases m2 moves out of phase with m1 until at around 9.5 Hz it is 180° out of phase with m1, maximizing the damping effect by maximizing the amplitude of x2 − x1, this maximizes the energy dissipated into c2 and simultaneously pulls on the primary mass in the same direction as the motor mounts.

## Mass dampers in automobiles

### Motorsport

The tuned mass damper was introduced as part of the suspension system by Renault on its 2005 F1 car (the Renault R25), at the 2005 Brazilian Grand Prix. The system reportedly reduced lap times by 0.3 seconds: a phenomenal gain for a relatively simple device.[1] The stewards of the meeting deemed it legal, but the FIA appealed against that decision.

Two weeks later, the FIA International Court of Appeal deemed the mass damper illegal.[2][3] It was deemed to be illegal because the mass was not rigidly attached to the chassis; the influence the damper had on the pitch attitude of the car in turn affected the gap under the car and the ground effects of the car. As such, the damper was considered to be a movable aerodynamic device and hence an illegal influence on the performance of the aerodynamics.

### Production cars

Tuned mass dampers are widely used in production cars, typically on the crankshaft pulley to control torsional vibration and, more rarely, the bending modes of the crankshaft. They are also used on the driveline for gearwhine, and elsewhere for other noises or vibrations on the exhaust, body, suspension or anywhere else. Almost all modern cars will have one mass damper, and some may have ten or more.

The usual design of damper on the crankshaft consists of a thin band of rubber between the hub of the pulley and the outer rim. This device, often called a harmonic damper, is located on the other end of the crankshaft opposite of where the flywheel and the transmission is. An alternative design is the centrifugal pendulum absorber which is used to reduce the internal combustion engine's torsional vibrations.

All four wheels of the Citroën 2CV incorporated a tuned mass damper (referred to as a "Batteur" in the original French) of very similar design to that used in the Renault F1 car, from the start of production in 1949 on all four wheels, before being removed from the rear and eventually the front wheels in the mid 1970s.

## Mass dampers in bridges

Tuned mass damper inside bridge deck of the Jan Linzelviaduct[4]

The tuned mass damper is widely being used as a method to add damping to bridges. One use-case for tuned mass dampers in bridges is to prevent large vibrations due to resonance with pedestrian loads.[5] By adding a tuned mass damper, damping is added to the structure which causes the vibration of the structure to be reduced as the vibration steady state amplitude is inversely proportional to the damping of the structure.

## Mass dampers in spacecraft

One proposal to reduce vibration on NASA's Ares solid fuel booster was to use 16 tuned mass dampers as part of a design strategy to reduce peak loads from 6g to 0.25g, with the TMDs being responsible for the reduction from 1g to 0.25g, the rest being done by conventional vibration isolators between the upper stages and the booster.[6][7]

Spin stabilized satellites have nutation development at specific frequencies. Eddy current nutation dampers have flown on spin stabilized satellites to reduce and stabilize nutation.

## Dampers in power transmission lines

The small black objects attached to the cables are Stockbridge dampers on this 400 kV power line near Castle Combe, England

High-tension lines often have small barbell-shaped Stockbridge dampers hanging from the wires to reduce the high-frequency, low-amplitude oscillation termed flutter.[8][9]

## Dampers in wind turbines

A standard tuned mass damper for wind turbines consists of an auxiliary mass which is attached to the main structure by means of springs and dashpot elements. The natural frequency of the tuned mass damper is basically defined by its spring constant and the damping ratio determined by the dashpot. The tuned parameter of the tuned mass damper enables the auxiliary mass to oscillate with a phase shift with respect to the motion of the structure. In a typical configuration, an auxiliary mass hung below the nacelle of a wind turbine supported by dampers or friction plates.[citation needed]

## Dampers in buildings and related structures

Location of Taipei 101's largest tuned mass damper

When installed in buildings, dampers are typically huge concrete blocks or steel bodies mounted in skyscrapers or other structures, which move in opposition to the resonance frequency oscillations of the structure by means of springs, fluid, or pendulums.

### Sources of vibration and resonance

Unwanted vibration may be caused by environmental forces acting on a structure, such as wind or earthquake, or by a seemingly innocuous vibration source causing resonance that may be destructive, unpleasant or simply inconvenient.

#### Earthquakes

The seismic waves caused by an earthquake will make buildings sway and oscillate in various ways depending on the frequency and direction of ground motion, and the height and construction of the building. Seismic activity can cause excessive oscillations of the building which may lead to structural failure. To enhance the building's seismic performance, a proper building design is performed engaging various seismic vibration control technologies. As mentioned above, damping devices had been used in the aeronautics and automobile industries long before they were standard in mitigating seismic damage to buildings. In fact, the first specialized damping devices for earthquakes were not developed until late in 1950.[10]

#### Mechanical human sources

Dampers on the Millennium Bridge in London. The white disk is not part of the damper.

Masses of people walking up and down stairs at once, or great numbers of people stomping in unison, can cause serious problems in large structures like stadiums if those structures lack damping measures.

#### Wind

The force of wind against tall buildings can cause the top of skyscrapers to move more than a meter. This motion can be in the form of swaying or twisting, and can cause the upper floors of such buildings to move. Certain angles of wind and aerodynamic properties of a building can accentuate the movement and cause motion sickness in people. A TMD is usually tuned to its building's resonant frequency to work efficiently. However, during their lifetimes, high-rise and slender buildings may experience natural resonant frequency changes under wind speed, ambient temperature and relative humidity variations, among other factors, which requires a robust TMD design.[11]

### Examples of buildings and structures with tuned mass dampers

Australia
• Sydney Tower in Sydney, Australia - has a water tank used to dampen oscillations from high winds and potentially from earthquakes. "Engineering and Construction of the Sydney Tower".
China
Czech republic
Taiwan
• Taipei 101 skyscraper — 660 metric tons (730 short tons) damper, formerly the world's heaviest.[13] Located on 87th to 92nd floors.
Germany
India
Iran
Ireland
Japan
Kazakhstan
Russia
United Arab Emirates
United Kingdom
United States

## References

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2. ^ Bishop, Matt (2006). "The Long Interview: Flavio Briatore". F1 Racing (October): 66–76.
3. ^ "FIA bans controversial damper system". Pitpass.com. 21 July 2006. Retrieved 2010-02-07.
4. ^ "Jan Linzelviaduct – Tuned Mass Damper". Flow engineering. Retrieved 2022-08-03.
5. ^ Heinemeyer, Cristoph; Butz, Christiane; Keil, Andreas; Schlaich, Mike; Goldbeck, Arndt; Trometor, Stefan; Lukic, Mladen; Chabrolin, Bruno; Lemaire, Armand (2009-10-01). "Design of Lightweight Footbridges for Human Induced Vibrations". JRC Publications Repository. Retrieved 2022-08-03.
6. ^ "Ares I Thrust Oscillation meetings conclude with encouraging data, changes". NASASpaceFlight.com. 2008-12-09. Retrieved 2010-02-07.
7. ^ "Shock Absorber Plan Set for NASA's New Rocket". SPACE.com. 2008-08-19. Retrieved 2010-02-07.
8. ^ Sauter, D; Hagedorn, P (December 2002). "On the hysteresis of wire cables in Stockbridge dampers". International Journal of Non-Linear Mechanics. 37 (8): 1453–1459. Bibcode:2002IJNLM..37.1453S. doi:10.1016/S0020-7462(02)00028-8. INIST:13772262.
9. ^ "Cable clingers – 27 October 2007". New Scientist. Archived from the original on 5 May 2008. Retrieved 2010-02-07.
10. ^ Reitherman, Robert (2012). Earthquakes and Engineers: An International History. Reston, VA: ASCE Press. ISBN 9780784410714. Archived from the original on 2012-07-26.
11. ^ Aly, Aly Mousaad (25 June 2014). "Proposed robust tuned mass damper for response mitigation in buildings exposed to multidirectional wind". The Structural Design of Tall and Special Buildings. 23 (9): 664–691. doi:10.1002/tal.1068. S2CID 108930033.
12. ^ Sial. Švácha, Rostislav., Beran, Lukáš, 1978-, Muzeum umění Olomouc., SIAL architekti a inženýři (Firm) (1st ed.). Olomouc: Arbor vitae. 2010. pp. 50–61. ISBN 9788087164419. OCLC 677863682.`{{cite book}}`: CS1 maint: others (link)
13. ^ taipei-101.com.tw
14. ^ "India Unveils 'Statue of Unity' - The Worlds Largest Statue". Born to Engineer. 2018-11-02. Retrieved 2022-04-01. Two 250 tonne tuned mass dampers were placed at chest height to control the sway in high winds.
15. ^ "The Statue of Unity | Sardar Patel | L&T". 2019-03-23. Archived from the original on 2019-03-23. Retrieved 2022-04-01. To arrest any sway of such a tall structure, two Tuned Mass Dampers of 250 tonnes each have been used.`{{cite web}}`: CS1 maint: bot: original URL status unknown (link)
16. ^ RIBBON CHAPEL on Vimeo
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18. ^ Luca, Septimiu-George; Pastia, Cristian; Chira, Florentina (2007). "Recent Applications of Some Active Control Systems to Civil Engineering Structures". The Bulletin of the Polytechnic Institute of Jassy, Construction. Architecture Section. 53 (1–2): 21–28.
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20. ^ Stewart, Aaron. "In Detail> 432 Park Avenue". The Architect's Newspaper. Archived from the original on 4 March 2016. Retrieved 31 January 2016.
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22. ^ "Comcast Center" (PDF). Archived from the original (PDF) on February 17, 2012. Retrieved 2010-02-07.
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24. ^ Staff (August 2011) "One Madison Park, New York City" Council on Tall Buildings and Urban Habitat website. Archived 28 January 2018 at the Wayback Machine.