Frequency Response Function |X₁/F| vs Frequency
fn1 = —
System Parameter Summary
—
fn1 Primary Natural Frequency [Hz]
—
fn2 TMD Natural Frequency [Hz]
—
μ Mass Ratio [–]
—
fopt Optimal TMD Frequency [Hz]
Theory Note — Dynamic Absorber (TMD) Principle
A tuned mass damper works by attaching a secondary mass tuned near the primary system's natural frequency, splitting the single resonance peak into two smaller peaks and driving the response near the original resonance frequency toward zero (anti-resonance).
$$f_{TMD}^{opt} = \frac{f_{n1}}{1+\mu}, \quad \zeta_{TMD}^{opt} = \sqrt{\frac{3\mu}{8(1+\mu)^3}}$$
Den Hartog (1956) optimal tuning rule. A larger mass ratio μ yields better vibration suppression, but involves trade-offs with design constraints (weight and space). In skyscraper TMDs (e.g., Taipei 101) μ ≈ 0.3–0.5% is typical.