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