Tuned Mass Damper
A tuned mass damper, or harmonic absorber, is a device mounted in structures to prevent discomfort, damage or outright structural failure by vibration. 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. High-tension lines often have small barbell-shaped Stockbridge dampers hanging from the wires[1][2].
Sources of vibration and resonanceUnwanted 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. EarthquakesThe seismic waves caused by an earthquake will make tall 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 oscillations of the building which may lead to structural failure. 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 dampening 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. WindThe 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. How they work
Tuned mass dampers stabilize against violent motion caused by harmonic vibration. The presence of a tuned damper allows the inertia of a great mass to be balanced by a comparatively lightweight structural component, such as a heavy concrete block placed in such a way that the block moves in one direction as the structure moves in the other, thus damping the structure's oscillation. The counterweight may be mounted using massive spring coils and hydraulic dampers. If the axis of the vibration is fundamentally horizontal or torsional, leaf springs and pendulum-mounted weights are employed. Tuned mass dampers are engineered, or "tuned" to specifically counter harmful frequencies of oscillation or vibration. 
This system consists of a main mass m1, such as a wheel and suspension arm, with a spring and damper k1/c1 between it and the body. The force into the body is F0, this is what we are trying to minimise. A variable force F1 is applied to m1, this is the excitation force. The system is modified by adding another spring/damper/mass system k2/c2 and m2. 
The graph shows the effect of a Tuned mass damper on a simple spring/mass/damper system, excited by a 1 N force applied to the main mass. The important measure for this system is the ratio of the force applied to the body, F0, as a result of F1. The blue line represents the baseline system, with a maximum response of 9 N into the base at 9 Hz. 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 N, at 7 Hz. The relative 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 proportion of the baseline mass used in the damper. 
The Bode plot is more complex, showing the phase and magnitude of the motion of each mass, for the two cases, relative to F1. The black line is for the baseline, and only shows the motion of m1. The blue line is the motion of m2 in the case with the tuned mass absorber. It goes into resonance early, in phase with m1, but with a higher amplitude. Therefore some of the energy that would have been used to vibrate the body (via F0) is absorbed in the damping element at c2. As the frequency increases m2 starts to move out of phase with m1, until at around 9.5 Hz it is moving in antiphase with m1, thereby pumping maximum energy into the damper at c2. Examples of buildings and structures with tuned mass dampers
Mass dampers in motorsportThe 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. Mass dampers in production carsTuned 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. References
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