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Vibration, Shock & MIL-Spec

PSD Grms · Miles' equation · transmissibility · natural frequency · shock · fatigue

PSD Profile Editor & Grms

Random-vibration spectrum. Edit breakpoints or load a MIL-STD-810 preset. Grms = √∫W(f)df, integrated segment-by-segment on the log-log profile.
Preset levels are representative examples for estimation — verify against the controlling spec.
Freq (Hz)PSD (G²/Hz)
— overall Grms

Miles' Equation — Resonant Response

RMS & 3σ peak acceleration of an SDOF at resonance under broadband random input.

Transmissibility & Isolation

T(r) curve and the √2 isolation crossover. Static deflection ↔ fn.

Natural Frequency Library

fn for common mounts. E entered in GPa, mass in grams.

Shock Loads

Peak force F = m·G·g, bracket bending and fastener shear under a shock pulse.
Bracket bending σ = 6FL/bh²
Fastener shear τ = F/(n·πd²/4)

SRS Estimate & Qual Margin

Quick SRS response bands and acceptance→qualification uplift (×√2, +6 dB).

Narrow-Band Fatigue Life

Tlife = 1 / (fn · P(σ>σallow)) and test-time equivalence.
Test-time equivalence
Formula reference

Grms = √∫W(f)df; sloped segment √(W₁f₁/(N+1)·[(f₂/f₁)^(N+1)−1]), N = (dB/oct)/3.01.

Miles: Grms = √(π/2·fₙ·Q·W₀), peak = 3×. T(r)=√[(1+(2ζr)²)/((1−r²)²+(2ζr)²)], r=f/fₙ.

fₙ=15.76/√δ(mm); cantilever fₙ=(1/2π)√(3EI/mL³); SS beam fₙ=(π/2L²)√(EI/ρA); plate fₙ=(π/2)√(D/ρh)(m²/a²+n²/b²).

F=mGg; bracket σ=6FL/bh²; fastener τ=F/(n·πd²/4); SRS peak ≈ 1.7·A; qual = acceptance·√2 (+6 dB).