Civil
Tuned Mass Damper
Auxiliary mass on springs that absorbs structural vibration at a specific frequency
A tuned mass damper (TMD) is an auxiliary mass connected by springs and dashpots to a primary structure. Sized so its natural frequency matches a problematic mode of the structure, the TMD oscillates out of phase with the structure, dissipating energy and reducing peak amplitude. Applications include skyscraper sway, pedestrian-bridge bouncing, wind-induced antenna vibration, and turbine-blade flutter. The Taipei 101 building hangs a 660-tonne steel sphere in its upper floors. Effective design requires accurate knowledge of the target frequency, damping ratio, and mass ratio—mistuning halves the benefit.
- FunctionCounter-oscillating mass
- Frequency matchTuned to target mode
- Mass ratio1-5% of structure
- Famous TMDTaipei 101 (660 tonnes)
- Optimal dampingDen Hartog tuning
- SensitivityMistuning halves effect
Interactive visualization
Press play, or step through manually. The visualization is yours to drive — try it before reading on.
Watch the 60-second explainer
A condensed visual walkthrough — narrated, captioned, under a minute.
Why tuned mass dampers matter
- Skyscrapers. Limiting wind- and earthquake-induced sway.
- Footbridges. Suppressing pedestrian-induced lateral oscillation.
- Long-span bridges. Damping flutter and vortex-induced vibration.
- Wind turbines. Tower and blade vibration control.
- Antennas and chimneys. Reducing wind-induced fatigue.
- Cars. Engine mounts, drivetrain absorbers.
- Industrial machinery. Press isolators, machine-tool stages.
Common misconceptions
- Always reduces vibration. Mistuned TMDs can amplify some frequencies.
- Heavier is always better. Diminishing returns past 5% mass ratio.
- One TMD covers all modes. Each mode needs its own tuning.
- Static analysis suffices. Dynamic, frequency-domain analysis is essential.
- Damping is the whole story. Stiffness matching matters more.
- Cheap retrofit. Installation costs scale with size; multi-tonne TMDs are major projects.
Frequently asked questions
How does a TMD work?
When the main structure oscillates at the target frequency, the TMD—tuned to the same frequency—lags by 90 degrees and pushes back through its springs, applying a force opposite to the structure's motion. The dashpot dissipates the energy as heat. The structure's response splits into two smaller peaks at frequencies above and below the original, with much lower amplitude than without the TMD.
How is the TMD sized?
Mass ratio (TMD mass / effective modal mass) typically 1-5%. Larger ratios give more robust performance but require massive auxiliary structures. Tuning frequency: f_TMD = f_structure / (1 + μ), where μ is mass ratio. Damping ratio: ζ ≈ √(3μ/8(1+μ)). These Den Hartog formulas minimize peak response under harmonic excitation.
What's the Taipei 101 damper?
A 5.5 m diameter steel sphere weighing 660 tonnes hangs from cables in floors 87-92, suspended like a giant pendulum. It tunes to about 0.15 Hz, matching the building's first mode. During Typhoon Soudelor (2015) it swung over a meter. Visible from a public observation deck, it's now a tourist attraction. Two smaller TMDs sit at the spire's tip.
Why did the Millennium Bridge need TMDs?
When opened in June 2000, the London Millennium Footbridge swayed laterally as pedestrians synchronized their gait with the motion in a positive feedback loop. It closed two days later. After two years of analysis and retrofit, 89 viscous dampers and TMDs were installed to absorb the lateral mode at 0.5 Hz. It reopened in 2002 and has been stable since.
What's a pendulum TMD?
A heavy mass swinging on cables or a pivot, tuned by adjusting cable length: f = (1/2π)√(g/L). Pendulums need only a fraction of the height for low frequencies and are common in supertall buildings where vertical space exists. A horizontal viscous damper between the mass and structure dissipates energy.
What's a sloshing damper?
A partially-filled water tank tuned so the natural sloshing frequency matches a structural mode. Cheap, no moving parts, simple to maintain. Used in mid-rise buildings, towers, and even ships. The Comcast Center in Philadelphia uses a 1,300-ton water-based TMD. Effective damping is added by baffles that increase viscous losses in the sloshing fluid.
What if the target frequency changes?
TMDs are sensitive to mistuning—a 5% frequency mismatch can cut effectiveness in half. Active and semi-active TMDs adjust stiffness or damping in real time using sensors and actuators, retuning to the actual mode. Magnetorheological dampers offer fast adjustment. Multiple TMDs at slightly different frequencies provide robustness against tuning drift.