Tuned mass damper

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Tuned mass damper atop Taipei 101 Tuned mass damper - Taipei 101 - Wikimania 2007 0224.jpg
Tuned mass damper atop Taipei 101
Shanghai Tower tuned mass damper 20191222Shang Hai Zhong Xin Zu Ni Qi .jpg
Shanghai Tower 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.

Contents

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 Spring-mass-damper system.svg
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 ( html.skin-theme-clientpref-night .mw-parser-output div:not(.notheme)>.tmp-color,html.skin-theme-clientpref-night .mw-parser-output p>.tmp-color,html.skin-theme-clientpref-night .mw-parser-output table:not(.notheme) .tmp-color{color:inherit!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output div:not(.notheme)>.tmp-color,html.skin-theme-clientpref-os .mw-parser-output p>.tmp-color,html.skin-theme-clientpref-os .mw-parser-output table:not(.notheme) .tmp-color{color:inherit!important}} 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. Tuned mass damper.png
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. 2dof plots.png
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 are. 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 Tuned mass damper inside jan linzelviaduct.jpg
Tuned mass damper inside bridge deck of the Jan Linzelviaduct

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. [6]

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. [7] [8]

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 Stockbridge dampers on an English 400 KV line arp.jpg
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. [9] [10]

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 ]

Location of Taipei 101's largest tuned mass damper Taipei 101 Tuned Mass Damper.png
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. [11]

Mechanical human sources

Dampers on the Millennium Bridge in London. The white disk is not part of the damper. London Millennium Bridge - Damper beneath deck, north side - 240404.jpg
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.

Examples of buildings and structures with tuned mass dampers

Australia
Canada
China
Czech republic
Taiwan
Germany
India
Iran
Ireland
Japan
Kazakhstan
Russia
United Arab Emirates
United Kingdom
United States

See also

Related Research Articles

<span class="mw-page-title-main">Resonance</span> Tendency to oscillate at certain frequencies

Resonance is the phenomenon, pertaining to oscillatory dynamical systems, wherein amplitude rises are caused by an external force with time-varying amplitude with the same frequency of variation as the natural frequency of the system. The amplitude rises that occur are a result of the fact that applied external forces at the natural frequency entail a net increase in mechanical energy of the system.

<span class="mw-page-title-main">Millennium Bridge, London</span> Bridge over the River Thames in England

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<span class="mw-page-title-main">Shock absorber</span> Mechanical component

A shock absorber or damper is a mechanical or hydraulic device designed to absorb and damp shock impulses. It does this by converting the kinetic energy of the shock into another form of energy which is then dissipated. Most shock absorbers are a form of dashpot.

<span class="mw-page-title-main">Tacoma Narrows Bridge (1940)</span> Suspension bridge in Washington, US, collapsed in 1940

The 1940 Tacoma Narrows Bridge, the first bridge at this location, was a suspension bridge in the U.S. state of Washington that spanned the Tacoma Narrows strait of Puget Sound between Tacoma and the Kitsap Peninsula. It opened to traffic on July 1, 1940, and dramatically collapsed into Puget Sound on November 7 of the same year. The bridge's collapse has been described as "spectacular" and in subsequent decades "has attracted the attention of engineers, physicists, and mathematicians". Throughout its short existence, it was the world's third-longest suspension bridge by main span, behind the Golden Gate Bridge and the George Washington Bridge.

Torsional vibration is the angular vibration of an object - commonly a shaft - along its axis of rotation. Torsional vibration is often a concern in power transmission systems using rotating shafts or couplings, where it can cause failures if not controlled. A second effect of torsional vibrations applies to passenger cars. Torsional vibrations can lead to seat vibrations or noise at certain speeds. Both reduce the comfort.

<span class="mw-page-title-main">Vortex shedding</span> Oscillating flow effect resulting from fluid passing over a blunt body

In fluid dynamics, vortex shedding is an oscillating flow that takes place when a fluid such as air or water flows past a bluff body at certain velocities, depending on the size and shape of the body. In this flow, vortices are created at the back of the body and detach periodically from either side of the body forming a Kármán vortex street. The fluid flow past the object creates alternating low-pressure vortices on the downstream side of the object. The object will tend to move toward the low-pressure zone.

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<span class="mw-page-title-main">Stockbridge damper</span> Tuned mass damper used to suppress wind-induced vibrations

A Stockbridge damper is a tuned mass damper used to suppress wind-induced vibrations on slender structures such as overhead power lines, long cantilevered signs and cable-stayed bridges. The dumbbell-shaped device consists of two masses at the ends of a short length of cable or flexible rod, which is clamped at its middle to the main cable. The damper is designed to dissipate the energy of oscillations in the main cable to an acceptable level.

<span class="mw-page-title-main">Mechanical resonance</span> Tendency of a mechanical system

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<span class="mw-page-title-main">Conductor gallop</span> High-amplitude, low-frequency oscillation of overhead power lines due to wind

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<span class="mw-page-title-main">Vibration</span> Mechanical oscillations about an equilibrium point

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<span class="mw-page-title-main">Harmonic damper</span>

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<span class="mw-page-title-main">Centrifugal pendulum absorber</span>

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<span class="mw-page-title-main">Ark Hills Sengokuyama Mori Tower</span> Skyscraper in Tokyo, Japan

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References

  1. ↑ "How Renault Won a World Championship by Creating a Tuned Mass Damper". Moregoodink.com. Retrieved 2019-02-08.
  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. ↑ Akkas, Kaan; Bayindir, Cihan (2023-10-13). "Efficient measurement of floating breakwater vibration and controlled vibration parameters using compressive sensing". Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment. doi:10.1177/14750902231203777. S2CID   264110144 . Retrieved 2023-10-14.
  7. ↑ "Ares I Thrust Oscillation meetings conclude with encouraging data, changes". NASASpaceFlight.com. 2008-12-09. Retrieved 2010-02-07.
  8. ↑ "Shock Absorber Plan Set for NASA's New Rocket". SPACE.com. 2008-08-19. Retrieved 2010-02-07.
  9. ↑ 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.
  10. ↑ "Cable clingers – 27 October 2007". New Scientist. Archived from the original on 5 May 2008. Retrieved 2010-02-07.
  11. ↑ Reitherman, Robert (2012). Earthquakes and Engineers: An International History. Reston, VA: ASCE Press. ISBN   9780784410714. Archived from the original on 2012-07-26.
  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. ↑ ACS, Matthew Allard (November 24, 2015). "RIBBON CHAPEL" – via Vimeo.
  17. ↑ Nakamura, Hiroshi (4 February 2015). "Ribbon Chapel / Hiroshi Nakamura & NAP Architects". ArchDaily. Retrieved 2017-02-15.
  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.
  19. ↑ "Tapering Begins as 111 West 57th Street Reaches for 1,428-Foot Pinnacle". 18 April 2018.
  20. ↑ Stewart, Aaron. "In Detail> 432 Park Avenue". The Architect's Newspaper. Archived from the original on 4 March 2016. Retrieved 31 January 2016.
  21. ↑ Petroski, Henry (1996). Invention by Design: How Engineers Get from Thought to Thing . Harvard University Press. pp.  205–208. ISBN   9780674463677.
  22. ↑ "Comcast Center" (PDF). Archived from the original (PDF) on February 17, 2012. Retrieved 2010-02-07.
  23. ↑ Bob Fernandez (December 10, 2014). "Engineers on the rise: Four young professionals tackle a career-making project". philly.com. Philadelphia Media Network (Digital), LLC. Archived from the original on November 22, 2017. Retrieved December 3, 2017.
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