Tuned mass dampers

A tuned mass damper, also known as a harmonic absorber, is a device mounted in structures to reduce the amplitude of mechanical vibrations. Their application can prevent discomfort, damage, or outright structural failure. They are frequently used in power transmission, automobiles, and buildings.

Tuned mass dampers stabilize against violent motion caused by harmonic vibration. A tuned damper reduces the vibration of a system with a comparatively lightweight component so that the 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. An electrical analogue is an LCR circuit.

Given a motor with mass ${\displaystyle m_{1}}$ 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, ${\displaystyle k_{1}}$ and ${\displaystyle c_{1}}$. The force on the motor mounts is ${\displaystyle F_{0}}$. In order to reduce the maximum force on the motor mounts as the motor operates over a range of speeds, a smaller mass, ${\displaystyle m_{2}}$, is connected to ${\displaystyle m_{1}}$ by a spring and a damper, ${\displaystyle k_{2}}$ and ${\displaystyle c_{2}}$. ${\displaystyle F_{1}}$ is the effective force on the motor due to its operation.

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