| name | acoustic-fatigue |
| description | Acoustic fatigue — random acoustic loading on panels, SPL/OASPL, Miner's rule for random fatigue, Miles equation, panel response, jet engine exhaust, MIL-STD-1530, ESDU 84008. |
| metadata | {"priority":7,"promptSignals":{"phrases":["acoustic fatigue","sonic fatigue","acoustic loading","sound pressure level fatigue","panel acoustic response","jet noise fatigue"],"minScore":3}} |
Acoustic Fatigue — Complete Skill
Acoustic Loading Fundamentals
Sound Pressure Level (SPL):
SPL = 20 log₁₀(p_rms / p_ref) [dB; p_ref = 20 μPa in air]
Overall SPL (OASPL):
OASPL = 10 log₁₀[Σ 10^(SPL_i/10)] [dBSPL; sum over frequency bands]
Typical jet exhaust near field: OASPL = 155–175 dB
Power Spectral Density (PSD) of pressure:
G_p(f) = p_rms² / Δf [Pa²/Hz]; relates to SPL per Hz
Root mean square pressure:
p_rms = √[∫G_p(f)df] [Pa; integral over frequency range]
Structural Response to Random Acoustic Loading
Panel equation of motion (thin plate):
m ẍ + c ẋ + k x = p(x,y,t) [distributed pressure loading]
Modal approach: decompose response into structural modes
x(t) = Σ q_i(t) × φ_i(x,y) [q_i = modal coordinates; φ_i = mode shapes]
Frequency response of mode i:
H_i(f) = 1/[k_i × (1 - (f/f_i)² + 2jζ_i(f/f_i))]
k_i = modal stiffness; f_i = natural frequency; ζ_i = modal damping (typically 0.01–0.03)
RMS response (Miles equation — single mode approximation):
G_x,rms = √[π × f_n × G_p(f_n) / (4 × ζ)] [displacement PSD integrated at resonance]
Miles equation for acceleration:
a_rms = √[π × f_n³ × G_p(f_n) / (2 × m_modal² × ζ)] [m/s²]
Stress Response
Bending stress from acoustic loading on flat plate:
σ_rms = C_s × p_rms × (a/t)² [Pa; C_s = stress concentration factor for panel geometry]
For simply supported rectangular panel:
σ_max = (1.5 × p × a²) / t² [Pa; a = shorter side; t = thickness; uniform pressure]
PSD of stress:
G_σ(f) = |H_σ(f)|² × G_p(f) [Pa²/Hz]
σ_rms = √[∫G_σ(f)df]
Fatigue Analysis for Random Loading
Rayleigh Distribution of Stress Peaks
For narrow-band random process (response dominated by single mode):
Peak stress amplitudes follow Rayleigh distribution:
P(σ_a) = (σ_a/σ_rms²) × exp(-σ_a²/(2σ_rms²))
Expected number of peaks per second:
n_p = f_0 [Hz; center frequency of response]
Miner's Rule Integration (Rayleigh peaks)
Cumulative damage per unit time:
D/T = n_p × ∫₀^∞ [p(σ_a) / N(σ_a)] dσ_a
S-N curve: N(σ_a) = (σ_a / σ_f')^(-1/b) [b = fatigue exponent; σ_f' = fatigue strength coefficient]
Closed-form (Rayleigh distribution):
D/T = n_p / N_f(σ_rms) × [Γ(1 + 1/m) × 2^(1/m)]
m = S-N slope; Γ = gamma function; applicable when S-N is linear in log-log
Fatigue life:
T_failure = 1 / (D/T) [seconds]
Equivalent Constant Amplitude Stress (Simplified)
σ_eq = k × σ_rms [k ≈ 3.0 for 0.1% probability; k = 4.0 for 0.01%]
Use σ_eq in standard fatigue analysis
Acoustic Fatigue Sources
Jet engine exhaust:
OASPL profile: peaks 3–6 nozzle diameters downstream; noise spectrum peaks at Strouhal St ≈ 0.2
Near-field: 150–175 dB OASPL; far field: 140–165 dB at 10 m
Cavity resonance (bomb bays, wheel wells):
Rossiter modes: f_n = (U/L) × (n - α) / (M + 1/κ) [U = freestream; L = cavity length; M = Mach; α, κ empirical]
SPL peaks: 160–180 dB in cavities; major acoustic fatigue driver on fighter aircraft
Turbulent boundary layer (TBL):
Pressure PSD on aircraft skin: G_p ≈ τ_w² δ / (U_e) × f(kL) [τ_w = wall shear; δ = boundary layer thickness]
Typical: OASPL 130–145 dB on high-speed aircraft fuselage panels
Panel Design for Acoustic Fatigue
Structural countermeasures:
- Increase panel natural frequency above acoustic spectral peak: f_n = (π/2) √(D/m) × (1/a² + 1/b²)
D = Et³/[12(1-ν²)] [flexural rigidity]
- Add damping treatment: constrained layer damping; SMACWRAP; target ζ ≥ 0.03
- Reduce aspect ratio (a/b → 1.0 reduces fundamental mode stress)
- Frame/stiffener spacing: controls panel first mode frequency
Allowable OASPL (aircraft panels, Dural/Al alloy):
Without treatment: OASPL ≤ 135–140 dB for > 10⁷ cycle life
With damping: OASPL ≤ 145–150 dB
Standards and References
| Standard | Scope |
|---|
| MIL-STD-1530D | Aircraft structural integrity; acoustic fatigue requirement |
| MIL-HDBK-516C | Airworthiness certification criteria |
| ESDU 84008 | Acoustic fatigue; panel response analysis |
| ESDU 74020 | TBL pressure fluctuations |
| NASA SP-8002 | Acoustic loads on launch vehicles |
| DO-160G Section 7 | Acoustic environment testing |
Output
Provide: OASPL and spectral distribution [dB vs. Hz], panel natural frequency f_n [Hz] and mode shape, modal damping ζ, RMS stress σ_rms [MPa] (Miles equation), equivalent fatigue stress σ_eq [MPa], predicted cycles-to-failure N_f, fatigue life T [hours], Miner cumulative damage per 1000 hr, design recommendations (f_n target, damping treatment, panel sizing), and applicable standard (MIL-STD-1530, ESDU 84008).
