Langford Analytic · Knowledge Base

Miles Equation Reference

A quick reference for Miles equation — the formula, variables, validity conditions and typical use cases.

Random Vibration2 min read
referenceMiles equationSDOFRMSscreening

Miles Equation

a_rms = √(π × fn × G(fn) / (4 × ζ))

where:
  fn = natural frequency [Hz]
  G(fn) = input PSD at fn [g²/Hz]
  ζ = damping ratio
  a_rms = RMS acceleration [g]

For displacement:
  x_rms = a_rms / (2π × fn)²

Validity

  • Lightly damped (ζ < 5%)
  • Single dominant mode
  • Flat PSD near fn
  • Gaussian, stationary, linear
  • Screening only — not for final assessment