Subway Vibration Complaint in a Laboratory
Occupants of a first-floor research laboratory above a new subway line complain of vertical floor vibration at 16 Hz and of dust moving on optical benches. A triaxial accelerometer bonded to the concrete floor at the bench location gives a 16 Hz one-third-octave rms acceleration of 0.008 m/s². Individual train passes last 25 s and peak at 0.012 m/s²; there are 120 passes over an 18 h day. The background between trains is 0.0015 m/s². The laboratory specification is VC-C in the 1–80 Hz range. The accelerometer was mounted with beeswax and calibrated before the survey; cross-axis sensitivity is below 5%. The facility manager proposes to average the entire 18 h exposure and compare that average with VC-C, arguing that the trains are intermittent. The lab manager wants to know whether the floor fails and whether the optical bench or the building must be isolated.
1. Convert the 16 Hz rms acceleration to velocity and compare it with the VC-C criterion. Does the floor meet the specification?
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At 16 Hz, v = a/(2πf) = 0.008/(2π × 16) = 7.96 × 10^-5 m/s = 79.6 µm/s. VC-C at 16 Hz is 12.5 µm/s, so the measured velocity is about 6.4 times the criterion, or 16 dB above it. The floor does not meet VC-C. The peak pass value of 0.012 m/s² corresponds to about 119 µm/s, even farther above the criterion. The background of 0.0015 m/s² corresponds to about 14.9 µm/s, which is about 14.5 dB below the train level, so background correction is small.
2. Evaluate the facility manager's proposal to average over 18 h. What metric and averaging time are appropriate for this laboratory criterion?
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Averaging over 18 h is inappropriate for this criterion. The trains occupy only 120 × 25 s = 3000 s = 0.83 h, so an 18 h Leq would be dominated by quiet periods and would hide the repeated passes that annoy occupants and disturb benches. VC curves are normally compared with a short-term rms, often 1 s, or with the maximum pass level; for human exposure, an appropriate weighted VDV or 1-s rms is used. Use the 1-s rms during a pass, report the maximum and the number of events, and compare with VC-C. If using ISO 2631-2, apply the appropriate frequency weighting and decide whether the criterion is for annoyance or equipment.
3. Recommend the next measurement and mitigation steps, distinguishing building treatment from bench isolation.
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First confirm the measurement: check accelerometer mounting, cable noise, cross-axis, and whether 16 Hz is a floor resonance or a local bench resonance. Map the floor with a grid and measure at the bench support and at the slab. If the floor itself exceeds VC-C, the building path is dominant; if the bench support is much worse, isolate the bench. Practical mitigation for the optical bench is a pneumatic isolation system with a natural frequency well below 16 Hz, plus mass and restraint. Building mitigation, such as stiffening the floor or adding an isolation slab, is much more costly and should follow a modal study. Re-measure after mitigation at the same points and report the pass-by maximum.