TUNED MASS DAMPERS (TMDs)

The make-up of a tuned mass damper consists of an inertia element (a mass) and a suspension mechanism comprised of restoring and dissipative elements. The most commonly used suspension mechanism in TMDs is the parallel combination of coil springs and viscous dampers, but they can also be realized using other suspension mechanisms such as air, viscoelastic and pendulum. TMDs are variations of the more general tuned absorbers/dampers commonly used in treating narrow-band noise and vibration issues.

The schematic diagrams of a translational and a pendulum tuned mass dampers (the red, 2nd order systems) appended to a vibrating structure (resembled by the black, 2nd order system M1-K1-C1) is shown in Figure 1.

Figure 1 Schematic of a structure with TMD

Tuned Mass Dampers (TMDs) are tuned by setting their natural frequencies substantially equal to the resonant frequencies of the structure targeted for damping.

Tuned mass dampers (TMDs) come in various configurations. The commonality between all of them is their make-up which includes an inertia element (mass) suspended by a parallel combination of an energy dissipating (damping) device and a restoring mechanism.

Restoring Mechanism

In tuned mass dampers operating in vertical direction coil springs either by themselves as shown in Figure 2-a or in configuration with a horizontal pendulum as shown in Figure 2-b act as the restoring mechanism.

Figure 2-a Vertical tuned mass damper

Figure 2-b Vertical tuned mass damper with horizontal pendulum configuration

In lateral tuned mass dampers ( TMDs operating in horizontal direction) leaf springs, vertical pendulums either by themselves or in conjunctions with coil springs are used as the restoring elements. Figures 2-c and 2-d show lateral TMDs using leaf springs and spring-stabilized inverted pendulum as the restoring mechanisms, respectively.

Figure 2-c Lateral tuned mass damper

Figure 2-d  Lateral tuned mass damper with inverted pendulum configuration

If the required height of a lateral TMD associated with the above listed restoring mechanisms cannot be accommodated, the weight of the inertia element (mass) is supported by a set of linear guides and resilience is provided by compression coil springs.

Lateral tuned mass dampers operating in more than one direction, normally use steel wire-rope suspended pendulum as their restoring mechanism. The length of the steel wire-ropes set the tuning frequency of such tuned mass dampers. Such TMDs are commonly used in quieting the lateral vibration of tall structures such as high rises, airport control towers, and exhaust stacks. Figure 2-e shows a multi-directional lateral tuned mass damper using steel wire ropes as the restoring elements.

Figure 2-e  Pendulum tuned mass damper

Damping Mechanisms of Tuned Mass Dampers

Viscous damping is commonly used as the energy dissipation mechanism in TMDs. Such damping is provided by ‘laminar flow viscous damping units’ (dashpots) utilizing a high viscosity damping fluid, ‘turbulent flow viscous dampers’ using a low viscosity damping fluid, or magnetic dampers.

• Dashpots do not have temperature compensation mechanism built into their make-up. But the use of proper damping fluid as well as the novel design of the TMDs using dashpots as their energy dissipation devices, enable such tuned mass dampers to maintain their effectiveness when subject to large temperature variations. The advantages of dashpots are a) their simple design and being maintenance-free, and b) being multi-directional.
• Turbulent Flow Viscous Damping Units are similar in make up to shock absorbers on an automobile suspension system. Shock absorber type viscous dampers are one-directional. Moreover, they require periodic maintenance mainly in terms of replacing their seals which could leak after so many cycles of oscillation. The advantages of this type of damping devices are a) the temperature compensation mechanism built into their make-up, enabling them to be less sensitive to variation in temperature, and b) being able to provide long strokes.
• Magnetic dampers (eddy current dampers) dissipate energy via the motion of a conductor within a magnetic field.  These dampers are liquid-free, temperature independent, non-contact and thus nearly maintenance-free.
  

  Eddy current is induced in a conductor moving thru a magnetic field, generating a secondary magnetic field  inside the conductor. The magnetic force of the secondary magnetic field  opposes the magnetic force generated by primary  magnets resulting in damping force proportional to the relative velocity of the primary magnet and the conductor.

Tuned mass dampers are sized so that a) their inertia/mass is large enough to ensure their effectiveness, b) their resilience in conjunction with their inertia/mass realizes the desired tuning frequency, and c) optimal amount of energy dissipation capability (internal damping) is built into them so that they effectively damp the vibration of their target modes.

The frequency response functions of an underdamped structure without and with two different tuned mass dampers are shown in Figure 3. One TMD has a small and the other has a large mass ratio. The optimal value of damping ratio in the smaller TMD is in excess of 3 times less than the larger TMD.

Clear from Figure 3, increase in mass ratio (and the corresponding damping ratio) of a TMD increases the energy dissipation (damping) effectiveness as well as the bandwidth of that TMD. Moreover, increase in mass ratio lowers the TMD excursion (the motion of the TMD mass relative to the structure).

Figure 3 Frequency response functions of a structure without and with a small TMD and a large TMD

As stated earlier, when a structure cannot either take the weight of or accommodate an optimally sized tuned mass damper and/or more than one vibration mode of which are in need of damping, then an active tuned mass damper (ATMD) or an Active Mass Damper (AMD) is a more suitable choice.