Floating Slab Track Vibration Calculator
Urban Rail Transit & Acoustic Engineering: Model Floating Slab Track (FST) natural frequency, vibration transmissibility, resonant amplification, and insertion loss (IL).
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Natural Frequency & Acoustic Insertion Loss
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Floating Slab Track (FST) Vibration Isolation Acoustics
High-density urban metro tunnels running beneath residential apartments, recording studios, and concert halls require floating slab tracks to mitigate ground-borne noise and tactile structure-borne vibrations.
1. Transmissibility & Insertion Loss
The vibration force transmissibility $T_r(f)$ from train wheels to tunnel substrate is:
T_r(f) = √[ (1 + (2·ζ·r)²) / ( (1 - r²)² + (2·ζ·r)² ) ]
where $r = f / f_0$ and the acoustic insertion loss is $IL = -20 \log_{10}(T_r(f))$ dB.
Frequently Asked Questions
How does a Floating Slab Track (FST) isolate subway ground-borne vibration?
A floating slab track mounts a heavy reinforced concrete trackbed on soft resilient rubber bearings, polyurethane mats, or steel coil springs inside a tunnel invert. Operating as a low-pass mass-spring mechanical filter, it transmits quasi-static axle loads while blocking dynamic vibration frequencies above the system cutoff frequency (f_c = f_0 · √2).
What is the danger of low-frequency resonant amplification in FST designs?
At frequencies close to the slab tuning frequency ($f_0$), ground vibration is amplified rather than attenuated (negative insertion loss). FST designers must tune $f_0$ well below the critical building resonance and human tactile perception spectrum (typically designing $f_0 \le 6\text{--}12\text{ Hz}$).
Why are steel helical springs favored over elastomeric pads for sensitive hospital and concert hall transit crossings?
Steel springs achieve extremely low dynamic stiffness without excessive creep, enabling very low tuning frequencies ($f_0 \approx 5\text{--}7\text{ Hz}$) that provide over 20 to 30 dB of ground-borne noise attenuation across the audible secondary noise band (31.5–125 Hz).