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⚖️ Tuned Mass Damper Explorer
A resonant structure, a small secondary mass on a spring and damper. Change the TMD-to-structure mass ratio and watch Den Hartog's optimal tuning — and the resonance peak it tames — respond live. A bigger absorber mass buys a flatter, lower peak; a tiny one barely helps.
TMD
Live Result — Frequency Response
Optimal frequency ratio f = ωd/ωp—
Optimal damping ratio ζ—
Peak dynamic magnification—
Powered by the exact Den Hartog (1956) fixed-points
formulas (
engine/tmd.js) — independently re-verified before
publishing against a genuinely separate method: a brute-force 2D numerical
search that minimizes the resonance peak directly over (f, ζ), with no
reference to the closed-form equations. The two methods agreed to within the
numerical search's own resolution.Method
Den Hartog (1956)f_opt = 1/(1+μ); ζ_opt = √(3μ/(8(1+μ))) — "fixed-points" optimal tuning for an undamped primary structure.
Scope: undamped primary structure (the classical Den Hartog assumption — real structures have some inherent damping, which shifts the true optimum slightly; this is the textbook baseline case, not a substitute for project-specific optimization).