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tuned circuit

Electrically conducting pathway containing both inductance and capacitance elements. When these elements are connected in series, the circuit presents low electrical impedance to alternating current of the same frequency as the resonance frequency of the circuit and high impedance to current of other frequencies. The circuit's resonance frequency is determined by the values of inductance and capacitance. When the circuit elements are connected in parallel, the impedance is high at the resonance frequency and low at other frequencies. With their ability to pass only certain frequencies, tuned circuits are important in, for example, radio and television receivers.

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Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.

Tuned mass damper

A tuned mass damper, also known as an active mass damper (AMD) or harmonic absorber, is a device mounted in structures to prevent discomfort, damage, or outright structural failure caused by vibration. They are frequently used in power transmission, automobiles, and in buildings.

Example

Tuned mass dampers stabilize against violent motion caused by harmonic vibration. A tuned damper balances the vibration of a system with comparatively lightweight component so that the worst-case vibrations are less intense.

Consider a motor with mass $m_1$ 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, $k_1$ and $c_1$ . The force on the motor mounts is $F_0$ ; suppose we wish to reduce the maximum force on the motor mounts as the motor operates over a range of speeds.

Let $F_1$ be the effective force on the motor due to its operation. We will add a smaller mass, $m_2$ , connected to $m_1$ by a spring and a damper, $k_2$ and $c_2$ .

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, $m_1$ . An important measure of performance is the ratio of the force on the motor mounts to the force vibrating the motor, $F_0/F_1$ . (We are assuming 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 ( $m_2$ ).

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 ( $m_2 = 0$ ). Now considering $m_2 = m_1/10$ , 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 $m_2$ moves out of phase with $m_1$ until at around 9.5 Hz it is 180° out of phase with $m_1$ , maximizing the damping effect by maximizing the amplitude of $x_2-x_1$ , this maximizes the energy dissipated into $c_2$ 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 R25), at the 2005 Brazilian Grand Prix. It was deemed to be legal at first, and it was in use up to the 2006 German Grand Prix.

At Hockenheim, the mass damper was deemed by the FIA to be a moveable aerodynamic device due to the influence it had on the pitch attitude of the car, and hence, as a consequence, the performance of the aerodynamics.

The Stewards of the meeting deemed it legal, but the FIA appealed against that decision. 2 weeks later, the FIA International Court of Appeal deemed the mass damper illegal.

Production cars

Tuned mass dampers are widely used in production cars, typically on the crankshaft pulley to control torsional vibration and bending modes of the crankshaft, on the driveline for gearwhine, and other noises. They are also used on the exhaust, on the body and on the suspension, as in the 2CV example above. Almost all cars will have one mass damper, some may have 10 or more.

Mass dampers in spacecraft

NASA's Ares uses 16 spring/mass absorbers as part of a design strategy to reduce peak loads from 6g to 0.25 g. The spring/mass system is responsible for reducing the vibration from 1g to 0.25g.

Dampers in power transmission lines

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

Dampers in buildings and related structures

Typically, the dampers are huge concrete blocks mounted in skyscrapers or other structures, and moved 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.

Mechanical human sources

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. Vibration caused by heavy industrial machinery, generators and diesel engines can also pose problems to structural integrity, especially if mounted on a steel structure or floor. Large ocean going vessels may employ tuned mass dampers to isolate the vessel from its engine vibration.

Wind

The force of wind against tall buildings can cause the top of skyscrapers to move more than a metre. 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.

Examples of buildings and structures with tuned mass dampers

Bally’s to Bellagio, Bally’s to Caesars Palace, and Treasure Island to The Venetian Pedestrian Bridges in Las Vegas
Berlin Television Tower (Fernsehturm) — tuned mass damper located in the spire.
Bloomberg Tower/731 Lexington in New York
Burj al-Arab in Dubai — 11 tuned mass dampers.
Citigroup Center in New York City — Designed by William LeMessurier and completed in 1977, it was one of the first skyscrapers to use a tuned mass damper to reduce sway. Uses a concrete version.
Comcast Center in Philadelphia, PA — Contains the largest Tuned Liquid Column Damper (TLCD) in the world at 1,300 tons.
Dublin Spire in Dublin, Ireland — This narrow slender structure was designed with a tuned mass damper to ensure aerodynamic stability during a wind storm.
Grand Canyon Skywalk
John Hancock Tower in Boston — A tuned mass damper was added to it after it was built.
London Millennium Bridge — 'The Wobbly Bridge'
One Rincon Hill South Tower — First building in the United States to have a liquid tuned mass damper
One Wall Centre in Vancouver — It employs tuned liquid column dampers, at the time of its installation, a unique form of tuned mass damper.
Park Tower in Chicago — The first building in the United States to be designed with a tuned mass damper from the outset.
Random House Tower Uses two liquid filled tampers in New York City
Sakhalin-I — An offshore drilling platform
Shanghai World Financial Center in Shanghai, China
Taipei 101 skyscraper — Contains one of the world's largest tuned mass damper at 730-tons.
Trump World Tower in New York
Yokohama Landmark Tower