Supplemental damping using tuned mass dampers (and other energy dissipation strategies such as viscous and viscoelastic damping) are commonly used by structural engineers and architects as a means of mitigating the undesirable effects of dynamic loading on structures including alleviation of floor vibration induced by human activities as well as wind and seismic responses of buildings, towers, and bridges.

Damping effectiveness and robustness (bandwidth) of TMDs increase by increasing their mass ratios. On the flip side, TMDs with large mass ratios could become too big and too heavy for some applications. This is especially true in tuned damping of high-rises and tall structures in which even a TMD with the modest mass ratio of 1% becomes excessively large and massive, weighting hundreds of Tons. Accommodating such a massive TMD in the top floor a high-rise and supporting its weight could become a challenge.

Damping (energy dissipation) effectiveness of a TMD depends on a) the accuracy of its tuning, b) the extent of its internal damping, and c) the size of its mass relative to the modal mass of its target mode, i.e., its mass ratio.

Introducing an active element (an actuator) into the make-up of a tuned mass damper changes the device to an active tuned mass damper (ATMD). Proper control strategies enable ATMDs to overcome the shortcomings associated with passive TMDs.
With the use of an appropriate control scheme an active TMD

a) has a wider frequency range (bandwidth) than a comparable passive TMD and thus is more robust to tuning inaccuracies,

b) can self-tune itself,

c) possesses higher effectiveness in adding damping to its target mode,

d) has in-situ selectivity of its control objectives

i.  human comfort during low perturbation

ii. increased structural safety during severe perturbation

e) can add damping to more than one mode of vibration when multiple modes are in need of being damped. This eliminates the need for using multiple passive TMDs, each tuned to one of the target modes.

An active tuned mass damper (ATMD) is realized by introducing a controllable element e.g., a linear actuator, into the make-up of a passive tuned mass damper. The schematic shown below presents an ATMD with the active element U, appended to a structure.

Figure 1 shows the frequency response functions as well as transient responses of a single mode of a structure with no treatment, treated with a passive TMD with the mass ratio of 0.5%, and treated with an active TMD with the same mass ratio, i.e., 0.5%. With the gains of the controller in the active TMD moderate enough such that its excursion would be in par with that of the passive TMD, the active TMD exhibits twice as much damping effectiveness as that of the passive one.

Figure 1 FRFs and transient responses of a structure with no treatment, treated with a passive TMD (blue traces) and an active TMD (red traces) both with the mass ratio of 0.5%

Figure 2 shows the same responses as those of Figure 1 for a single mode of a structure with no treatment, treated with a passive TMD with the mass ratio of 0.5%, and treated with an active TMD half as massive as the passive unit having the mass ratio of 0.25%. With the gains of the controller in the active TMD moderate enough such that its excursion would only be twice as high as that of the passive TMD, the active TMD is exhibiting the same (or slightly better) damping effectiveness as that of the passive one.

Figure 2 FRFs and transient responses of a structure with no treatment, treated with a passive TMD with the mass ratio of 0.5% (blue traces) and treated with an active TMD with the mass ratio of 0.25% (red traces)

When adequate room is available to accommodate the excursion of an active TMD, the damping effectiveness as well as robustness of the ATMD can be increased by using larger control gains. This would make the ATMD applicable to multi-hazard mitigation situations with in-situ selectivity of its control objectives. That is, it would use small control gains when human comfort during noncritical times is the main objective and use large control gains when increased structural safety during severe dynamic loading becomes the objective.

Figure 3 FRFs of a structure without TMD (dotted black trace) and structure with an active TMD with 3 different control authorities

Figure 3 shows the frequency response functions (FRFs) of the first mode of a structure with and without an active TMD with three different control gains of ‘low’, ‘medium’ and ‘high’. The figures shows the capacity of an ATMD to selectively exhibit different levels of damping performance. In addition to achieving more effectiveness, the increase the control gain increases the frequency range (bandwidth) of the ATMD providing more robustness to tuning inaccuracies.

Figure 4 Multi-frequency tuning of an ATMD

Multi-Frequency Tuning: An ATMD can be tuned to more than one frequency eliminating the need for using multiple TMDs tuned to multiple frequencies. Moreover, an ATMD can be controlled so that it acts as a dynamic vibration absorber, quieting the forced vibration at an off-resonant frequency.

Figure 4 depicts the FRFs of a structure without (blue trace) and with (red trace) an ATMD tuned to three natural frequencies and one off-resonant frequency.

An ATMD has a higher initial cost than an equally sized passive TMD. But considering that a properly controlled active TMD is a) as effective as a passive TMD almost twice as large, b) more robust against detuning, c) capable of being tuned (add damping) to more than one mode of the structure, and d) applicable to multi-hazard mitigation situations it could be a very economically attractive solution in many applications.

ATMDs use smaller moving mass than passive TMDs with equivalent effectiveness. The cost saving associated with the smaller weight of a) the active TMD and b) its required support structure, would make up for the added cost associated with their actuation and controls.

ATMDs require external power to run, but realizing that an active TMD is basically a passive TMD with an added actuator, a portion of the vibration abatement objective is accomplished by the passive part of the active TMD. This would minimize their external power demand.

Active TMD Switchable to Passive TMD is an active tuned mass damper which under moderate dynamic loading and when most of vibration is at its target mode, turns its active element into a passive viscous damper and acts as a passive TMD. Also in the unlikely event of power loss, the active TMD reverts to a passive TMD offering some degree of effectiveness.

Once the vibration level of the structure, at its fundamental mode, reaches a certain threshold requiring more effectiveness than the passive TMD can deliver and/or more than one mode of the structure need to be damped, the active element is turned back on switching the device into an active TMD.

In its passive state, the active/passive switchable device is tuned to the first mode (fundamental mode) of the structure and acts as a passive TMD. In its active state, it possess all the attributes of an active tuned mass damper listed above.

Being active allows for the use of smaller moving mass and being able to switch to passive allows for less power consumption. As stated earlier, the cost saving due to the smaller weight would make up for the added cost of incorporating the active feature into this active/passive switchable TMD.

Semi-active TMDs  are simply adjustable passive TMDs that, thru the use of adjustment features/mechanisms, automatically re-adjust their parameters and stay optimally tuned to their target frequencies. Because of this continuous in-situ re-tuning (via the re-adjustment of stiffness and/or damping) the performance of semi-active TMDs is robust in the face of changes in the dynamics (and thus variation in natural frequencies) of their target structures.  DEICON’s Semi-active Air-Suspended Tuned Mass Damper is an example of such TMDs.

Being still a passive device (albeit with adjustability), semi-active TMDs are no more effective than a well-tuned passive TMD.

Figure 5  An active mass damper appended to a structure

Active Mass Damper (AMD) is a mass connected to the structure through an actuator. Compared to active tuned mass dampers, AMDs are more straightforward in their make-up; they use no springs and dampers. Moreover, AMDs can be used in broadband vibration abatement.

The schematic of Figure 7 shows the schematic of an active mass damper made up of a linear actuator and a mass (M₂), appended to a structure.  AC servomotors with ball screw mechanisms or hydraulic cylinders are candidate actuators for AMDs.

Figure 8 depicts the image of a 20,000 lb active mass damper. An AC servo-motor driving a ball screw linear motion system is used as the actuator of the AMD. Alternatively, a servo-hydraulic actuator could be used to drive the AMD.

Figure 6 A 20,000 lb active mass damper

Considering that the damping performance of any tuned damping device is directly proportional to the inertia force of its moving mass (product of mass, stroke, and frequency squared), extending the stroke up to the limit of the installation space allows for the reduction the weight of the moving mass, without changing its effectiveness.

The absence of passive springs and viscous dampers and the use of long stroke actuators enable AMDs to have smaller moving mass and thus weigh less than comparable TMDs or ATMDs. For example an AMD with the moving mass of 30 tons and the stroke of +/- 600 mm is as effective as a passive TMD with the moving mass of 60 tons and stroke of +/-300 mm. This dramatic reduction in weight would reduce the space requirement and structural reinforcement needed to install an AMD in many applications including civil engineering and marine structures.