Upon having the construction of a new church near completion, walking induced vibration was perceived on a long span balcony. DEICON conducted on-site measurements and identified the first two natural frequencies of the balcony. In addition, the participating mass and the damping ratio of mode 1 of the balcony was evaluated. Tuned damping was used to abate walking-induced vibration of the balcony.
Figure 1 Installed TMDs
Two tuned mass dampers (TMDs) with the nominal moving mass of 1400 lb (~600 Kg) each, both tuned to the first natural frequency of the balcony, were designed and built. The depth and height of the TMDs were chosen so that they fit within two existing W14x61 beams; see Figures 1 and 2. The remaining parameters of the TMDs namely their tuning frequency and damping ratios were selected based on the measured dynamic attributes of the balcony.
The blue traces in Figure 2 present the power spectral densities (PSDs) and time traces of the measured acceleration at two locations close to the edge of the balcony, in response to a heel drop at the center edge of the balcony, with the TMDs operational. The red traces show the measured data acquired in a similar fashion as that of blue traces except with the TMDs operational.
Figure 2 Power spectral densities and time traces of the measured vibration of the balcony at two locations without and with the TMDs operational
The extent of added damping to the balcony is estimated by fitting an exponential decay (with known damping and frequency) to the envelope of narrow-band filtered time traces measured at the center edge of the balcony; see Figure 3. As noted on Figure 3, the damping ratio of the mezzanine without the TMDs operational is estimated at 2% and with the TMDs operational is estimated at 11%. That is, the TMDs have increased the damping ratio of the mezzanine by more than 5 folds (500%).
Figure 3 Filtered acceleration time traces measured at the center of the balcony (solid blue and red lines) and their corresponding exponential decays (dotted black lines), with the TMDs locked (top plot) and the TMDs unlocked (bottom plot)