Tools › Structures › Fatigue › Random Vibration Fatigue › Example
NAVMAT P-9492 random vibration on a 100 Hz, Q = 10 structure: response rms, Miles' equation, spectral moments and the fatigue damage by Dirlik, narrow band, Steinberg and Wirsching–Light
| Tool | Random Vibration Fatigue |
| Source | U.S. Department of the Navy, Naval Material Command (1979). Navy Manufacturing Screening Program. NAVMAT P-9492, May 1979, Figure 5; Dirlik, T. (1985). Application of Computers in Fatigue Analysis. Ph.D. thesis, University of Warwick, Coventry, pp. 128–129; Bishop, N. W. M. (1988). The Use of Frequency Domain Parameters to Predict Structural Fatigue. Ph.D. thesis, University of Warwick, Coventry, eqs. 2.57–2.58 and 3.1–3.3; Miles, J. W. (1954). "On Structural Fatigue Under Random Loading." Journal of the Aeronautical Sciences, Vol. 21, No. 11, pp. 753–762; U.S. Department of Defense (2003). Metallic Materials and Elements for Aerospace Vehicle Structures. MIL-HDBK-5J, Figure 3.7.6.1.8(d). |
| Level | Graduate |
Problem
A structure with a natural frequency of 100 Hz and Q = 10 is mounted on a shaker running the NAVMAT P-9492 screening spectrum (0.04 g²/Hz from 80 to 350 Hz, 3 dB/octave slopes to 20 and 2000 Hz) for one hour; the stress at its critical point is 1 ksi per g of response acceleration and the material follows the MIL-HDBK-5J unnotched 7075-T6 sheet curve log N = 14.86 − 5.80 log S_eq, S_eq = S_max (1 − R)^0.49. Find the input rms, the response rms by Miles' equation and by integration, the spectral moments, the rates of zero crossings and peaks, the irregularity factor, the stress rms and the fatigue damage of the hour and the time to failure by the narrow-band, Dirlik, Steinberg and Wirsching–Light methods.
Inputs to Enter
- PSD breakpoints 20 Hz 0.01, 80 Hz 0.04, 350 Hz 0.04, 2000 Hz 0.007 g²/Hz; duration 1 h
- SDOF f_n = 100 Hz, Q = 10 (ζ = 0.05); σ_1g = 1 ksi per g, K_f = 1
- S-N: MIL-HDBK-5J Figure 3.7.6.1.8(d), A 14.86, B 5.80, C 0, p 0.49 (ksi), fully reversed (R = −1); life factor 1
Answers
- Input rms = 6.058 g (NAVMAT prints 6.0 g rms); the rising segment is +3.01 dB/octave, the falling one −3.01 dB/octave
- Miles' equation √(π f_n Q W/2) = 7.927 g rms; exact white-noise form with (1 + 1/Q²) 7.966 g; integration over the actual band 7.820 g rms
- m_0 = 61.15 g², m_1 = 6,078, m_2 = 628,642, m_4 = 1.2836 × 10¹⁰ (Hz-based); E[0] = 101.39 Hz, E[P] = 142.90 Hz, γ = 0.7096, x_m = 0.6956
- Stress rms 7.820 ksi; Dirlik D_1 0.2556, D_2 0.0662, D_3 0.6782, R −0.5125, Q 0.3195; Wirsching–Light λ = 0.7347
- Damage of the hour: narrow band 0.03052 (closed form = integral), Dirlik 0.02087, Steinberg 0.02238, Wirsching–Light 0.02242; time to failure 32.8 / 47.9 / 44.7 / 44.6 h
- Seeded 20,000 s time-domain simulation with rainflow counting gives 0.02084 per hour: Dirlik within 0.2 %, narrow band 46 % high, Steinberg and Wirsching–Light 7 % high
Notes
The tool's default inputs are this case; press Submit. The combination of profile, structure and material is illustrative (no published worked example combines them); each piece is checked against its source in test-scripts/test_random_vibration_fatigue.php (profile rms values of NAVMAT P-9492, NASA-HDBK-7005 and MIL-STD-810H, Miles' closed form, Dirlik's density and moments, the Wirsching–Light coefficients) and the whole against the numpy check and simulation in References/Random-Vibration/checks/.