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Miles' Equation

For random vibration, Miles' equation gives the 1σ acceleration response of a single-degree-of-freedom item to a flat PSD: G_rms = √((π/2)·f_n·Q·ASD). Design loads are normally taken at 3σ.

Natural frequency fn (Hz)

Damping ratio ζ

PSD / ASD (G²/Hz)

Component mass (kg)

Amplification Q

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1σ response

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3σ acceleration

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3σ inertia load

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Assumes a single dominant mode and a flat PSD around it. Q ≈ 1/(2ζ); Q = 10 (ζ = 5%) is a common default for bolted structures.

A helper, not a substitute for engineering judgment. Verify against the governing standard.