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 $m_1$ 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 $F_0$. In order to reduce the maximum force on the motor mounts as the motor operates over a range of speeds, a smaller mass, $m_2$, is connected to $m_1$ by a spring and a damper, $k_2$ and $c_2$. $F_1$ is the effective force on the motor due to its operation.
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, $\frac{F_0}{F_1}$. 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 baseline system has a maximum response of 9 units of force at around 9 units of frequency. Adding a tuned mass of 10% of the baseline mass reduces this maximum response to 5.5, at a frequency of 7.
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. 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 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.
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 information presented is based solely on the supplied corpus. No external sources were consulted beyond the provided text.
The maximum response of the baseline system is 9 units of force at around 9 units of frequency.
Adding a tuned mass of 10% of the baseline mass reduces this maximum response to 5.5, at a frequency of 7.
These figures are directly from the corpus.