Natural Frequency / Damping Random Response Illustration
An illustrative calculator showing how natural frequency and damping affect the Miles equation RMS response, demonstrating the sensitivity.
Calculator
Miles equation: a_rms = √( π × fn × G(fn) / (4 × ζ) ) Sensitivity to damping: a_rms ∝ 1/√ζ Halving ζ → a_rms × √2 ≈ 1.41 Sensitivity to fn (flat PSD): a_rms ∝ √fn Doubling fn → a_rms × √2 ≈ 1.41 Sensitivity to PSD: a_rms ∝ √G(fn) Doubling G → a_rms × √2 ≈ 1.41 Illustrative cases (G = 0.02 g²/Hz flat): fn=100, ζ=5%: a_rms = 5.60 g fn=100, ζ=2.5%: a_rms = 7.93 g (×1.41) fn=200, ζ=5%: a_rms = 7.93 g (×1.41) fn=100, ζ=1%: a_rms = 12.53 g (×2.24)
Assumptions
- Miles equation assumptions apply (SDOF, flat PSD, light damping)
- Illustrative — demonstrates sensitivity, not specific conclusions
- PSD assumed flat — actual PSD shape changes the fn sensitivity
Limitations
This calculator illustrates the sensitivity of the Miles equation result to each parameter. It does not produce engineering conclusions — the actual sensitivity in a specific case depends on the PSD shape, mode count and structure. Always evaluate sensitivity for the specific case.