Tuned dynamic absorbers and tuned mass dampers are reactive devices used in structural and acoustic systems to either absorb oscillation at a certain forcing frequency or damp oscillation at a particular resonant frequency, respectively. The make up of tuned absorbers and tuned dampers are for the most part the same, i.e., they are both made up of an inertia element (mass/inertance), a restoring element (spring/compliance), and an energy dissipating element (damper/sound absorbing material). What distinguishes one from the other is the extent of energy dissipation in their dissipative element. Tuned absorbers have negligible but tuned dampers have sizable amount of energy dissipation (damping).
In terms of applications, dynamic absorbers are used to abate the extent of a harmonic perturbation experienced by a structure (or an acoustic environment) and are tuned to the perturbation frequency. Tuned dampers are used to add tuned damping to a single mode of a structure (or a standing wave of an acoustic environment) and as such are tuned to the natural frequency of that mode (standing wave).
Tuned vibration absorbers (also known as tuned dynamic absorbers) and tuned mass dampers are the realizations of tuned absorbers and tuned dampers for structural vibration control applications. Their make up consist of inertial elements and resilient elements; what distinguishes tuned mass dampers from tuned vibration absorbers is the presence of dissipative elements in tuned mass dampers and lack there of in tuned vibration absorbers. Depending on the application, these devices are sized from a few ounces (grams) to many Tons. Other configurations such as pendulum absorbers/dampers, and sloshing liquid absorbers/dampers have also been used in vibration mitigation applications.
Figure 1 shows an underdamped structure (M1, K1, C1) with the resonant frequency of 9.5 Hz subject to a periodic excitation at the frequency of 35 Hz. A tuned mass damper (M2, K2, C2) tuned to the resonant frequency of the structure, i.e., 9.5 Hz and a tuned vibration absorber (M3, K3) tuned to the excitation frequency of 30 Hz are appended to the structure to mitigate its vibration.
Figure 1 Schematic of a structure treated with a tuned mass damper and a tuned vibration absorber
Figure 2 depicts the frequency response functions of the structure without (the black/dashed line trace) and with (the red/solid line trace) the vibration mitigation treatment.
Figure 2 Frequency response function of the structure without and with vibration treatment
Clear from Figure 2, tuned damping induced by the tuned mass damper and dynamic absorption induced by the tuned vibration absorber, are substantial.
Figure 3 A perforated liner
Helmholtz resonators, quarter-wave tubes, perforated liners, and passive acoustic radiators are the common realizations of tuned absorbers/dampers for acoustic applications. They are commonly used in narrow-band/tuned acoustic treatment of various architectural, industrial, and aerospace acoustic environments. Figure 3 shows the schematic of a perforated acoustic liner.
Tuning of Tuned Absorbers/Dampers
The parameters of a tuned absorber/damper are selected such that their natural frequencies match the disturbance frequency (for tuned absorption) or resonant frequency of a particular mode (for tuned damping) of an structural/acoustic system being treated. In case of tuned damping, as stated before, enough energy absorption (damping) should be built into the tuned damper so that the resonant mode targeted for damping does truly get damped rather than get split into two modes (one with a higher and one with a lower natural frequency of the tuned frequency).
Another important factor directly affecting the effectiveness of tuned absorbers/dampers in both structural and acoustic applications is the size of their inertia elements relative to the size of the structure/acoustic_system they are designed to treat. The larger the inertia element, the more effective the device. The inertia element of the tuned treatment is normally around 1 to 10% of the oscillating inertia they are meant to quiet.
Figure 4 shows the frequency response functions of a structure subject to a 30 Hz perturbation a) with no treatment (green trace), b) treated with a small dynamic vibration absorber (red trace) and c) treated with a large dynamic vibration absorber (black trace). The tuning frequency of dynamic vibration absorbers is the frequency corresponding to the notch on the frequency response function plot of Figure 4, i.e. 30 Hz. Note that the depth of the notch representing the effectiveness of the dynamic vibration absorber increases with increase in its mass.
Figure 4 Frequency response functions of a structure without and with two different tuned vibration absorbers
The width of the notch in Figure 4, presenting the bandwidth of the dynamic absorber, is rather narrow; the narrow bandwidth of dynamic absorber makes the accuracy of its tuning crucial. Although increase in the size of dynamic absorber widens the bandwidth somewhat but it does not diminish the importance of tuning accuracy. The accuracy of tuning becomes even more crucial considering that in addition to the notch (the desirable outcome) dynamic absorber introduces a peak with its resonant frequency very close to the frequency of the notch (the undesirable outcome). A small mis-tuning would match the frequency of the peak (instead of the frequency of the notch) with the perturbing frequency causing the structure to resonate rather becoming quit.
When the frequency of harmonic perturbation matches or is close to the resonant frequency of the structure (or acoustic environment), tuned damping is a more prudent solution than dynamic absorption is. Figure 5 shows the frequency response functions of a structure without any treatment (green trace), treated with a dynamic vibration absorber (red trace) and treated with a tuned mass damper (black trace). The resonant frequency of the structure is 10 Hz.
Figure 5 Frequency response functions of a structure without and with a tuned dynamic absorber and a tuned mass damper both tuned to the natural frequency of the structure
Figure 5 Frequency response functions of a structure without and with a DVA and a TMD both tuned to the natural frequency of the structure
A dynamic absorber is very effective in abating the resonant vibration of its target structure (or oscillation of its target acoustic system) at its tuning frequency corresponding to the notch on the red trace in Figure 5, but it also breaks the single resonant peak of the structure to two neighboring peaks (a phenomenon known as ‘mode splitting’). The presence of these two highly underdamped resonant peaks makes the accuracy of tuning very crucial. As stated earlier, mis-tuning could result in the structure (or acoustic system) resonating ra
ther than becoming quiet. A tuned damper tuned to the same frequency might not be as effective as an equivalent dynamic absorber at the tuning frequency but it has a wider bandwidth and does not split the target mode into two highly underdamped modes; see the black trace in Figure 5.
Active/Semi-active Tuned Absorbers/Dampers
A limitation of tuned absorbers/dampers is their tuning sensitivity related to the ﬂuctuation in the offending frequency of their controlled subject. Another limitation of tuned absorbers/dampers is their size. Active tuned absorbers/dampers address these issues.
Figure 6 An active tuned mass damper
Active tuned absorbers/dampers are realized by introducing active elements into the make-up of passive tuned absorber/dampers. Figure 5 shows the schematic of an active tuned mass damper with the active element (linear actuator) U.
Active tuned absorbers/dampers have higher effectiveness than their passive counterparts equivalent in size. and can readily be readjusted (re-tuned) via their electronics/software (manually or automatically). Moreover, a single active system can be tuned to multiple frequencies, simultaneously. They are also smaller in size than their passive counterparts.
An alternative to active tuned absorbers/dampers is semi-active tuned absorbers/dampers. These are passive devices with adjustability built into their make-up. By occasional re-adjustment of the adjustable parameters, such devices maintain their optimal tuning and remains effective, even when the structural parameters and loading conditions changes.