The irregular shape of three large, 1200 square feet, cantilevered balconies in a high-profile performing arts center resulted in areas at the balcony tip and edge susceptible to potentially annoying levels of vibration. To mitigate this effect, the building designers added tuned mass dampers (TMDs) to the underside of each of the three balconies.

Following the finite element modeling and actual measurement of the balconies vibration, the results of which were used to size the tuned dampers, nine passive tuned mass dampers were designed, built and installed on the three balconies. They were appended to the vibrating structure (the balconies) at locations where they could most effectively couple with the target mode(s). Figure 2 shows two of the TMDs installed underneath one of the balconies.

The TMDs were tuned to the first two modes of the balconies with the natural frequencies of 6 and 9 Hz. They were placed at locations where they could most effectively couple with their target modes; two TMDs at the edge and one at the tip of each balcony.

The TMDs effectively absorbed oscillatory energy of the structure and dissipated it internally, lowering the vibration due to human activities to an acceptable level. Figure 3 depicts the spectral and time traces of acceleration measured on the bottom balcony shown in Figure 1.

The blue trace in Figure 3 presents the response of the floor to a heel drop perturbation without the TMDs operational. The red and green traces depict the same measurement when the TMDs are brought online, one at a time.  Clear from Figure 3, tuned mass dampers have effectively dampened the structural mode they are tuned to dissipating its vibration.

When designed, built, installed, and tuned properly
TMDs effectively dissipate the resonant vibration of the
structure, reducing its undesirable motion.