Tuned Mass Damper (2D) | mysimulator.uk

Forcing

Forcing frequency ratio β = ω/ωn 1.00

Forcing amplitude 0.30

Building damping ζ₁ 2.0%

Tuned Mass Damper

Mass ratio μ = m₂/M 3.0%

Tuning ratio f₂/f₁ (1.0 = matched) 1.00

TMD damping ζ₂ 10.0%

Live Readout

Sway with TMD: —

Peak sway — TMD engaged

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Peak sway — no TMD

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Amplitude reduction

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How it works

The building's top floor is modeled as a mass-spring-damper oscillator driven by a periodic force (wind gusts or ground shaking): M·ẍ₁ + c₁·ẋ₁ + k₁·x₁ = F₀sin(ωt). Near resonance (β≈1) the sway amplitude would grow large. A tuned mass damper — a secondary mass m₂ on its own spring k₂ and damper c₂, the real 660-tonne pendulum atop Taipei 101 — is attached to the building. When its natural frequency f₂ is tuned close to the building's f₁, it oscillates out of phase and its damper bleeds off vibrational energy, cutting the building's sway. Mistune the ratio f₂/f₁ away from 1.0 and the cancellation weakens; toggle the TMD off to lock it out entirely and watch the amplitude climb back to the undamped case.

M·x1'' + c1·x1' + k1·x1 = F(t) + c2(x2'-x1') + k2(x2-x1)
m2·x2'' + c2(x2'-x1') + k2(x2-x1) = 0
optimal tuning (Den Hartog): f2/f1 ≈ 1/(1+μ)

Building sway — TMD engaged Building sway — no TMD (ghost)