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GEVS qualification random vibration on a 100 Hz component: profile rms, Miles' equation against the exact SDOF integral, 3σ levels and exceedance
| Tool | Random Vibration Response |
| Source | NASA Goddard Space Flight Center (2013). General Environmental Verification Standard (GEVS) for GSFC Flight Programs and Projects. GSFC-STD-7000A, 22 April 2013, Table 2.4-3; National Aeronautics and Space Administration (2001). Dynamic Environmental Criteria. NASA-HDBK-7005, eq. 5.27 and section 5.1.7; Irvine, T. (2000). Integration of the Power Spectral Density Function, Revision B. Vibrationdata. |
| Level | Professional |
Problem
A 10-lb component with a natural frequency of 100 Hz and Q = 10 is qualified to the GEVS generalized random vibration level (20 Hz 0.026 g²/Hz, +6 dB/oct to 50 Hz, 0.16 g²/Hz from 50 to 800 Hz, −6 dB/oct to 0.026 g²/Hz at 2000 Hz) for 120 s per axis. Find the input g rms by exact integration of the log-log segments, the response by Miles' equation and by the exact integral of the transmissibility over the profile, the 3σ acceleration, relative displacement and inertia load, the rate of zero crossings and 3σ crossings, the level exceeded with 1 % probability in the run, the expected largest peak, and the margin on a stress of 0.8 ksi per g against a 60 ksi allowable.
Inputs to Enter
- Profile: GEVS qualification (GSFC-STD-7000 Table 2.4-3); breakpoints 20 / 0.026, 50 / 0.16, 800 / 0.16, 2000 / 0.026 (Hz, g²/Hz)
- Component f_n 100 Hz, Q 10; duration 120 s; exceedance probability 1 %; design level k = 3
- Mass 10 lbm; stress per g 0.8 ksi, allowable 60 ksi, FS 1.0, limit level
Answers
- Segment areas 2.496 + 120.0 + 76.8 (the +6 dB/oct rise from 0.026 at 20 Hz, the plateau, the −6 dB/oct fall) = 199.82 g²; input 14.14 g rms (table prints 14.1 Grms; acceptance column 9.995 → 10.0)
- Miles: √[(π/2) · 100 · 10 · 0.16] = 15.85 g rms; exact white noise with (1 + 1/Q²): 15.93 g; integrated over the profile: 15.74 g rms (Miles/exact 1.007)
- E[0] = 101.3 zero up-crossings per second (12,155 cycles in 120 s), E[P] = 154.8 peaks per second, γ = 0.654; relative displacement 0.01531 in rms (Miles-based 0.01550 in)
- 3σ: 47.21 g, 0.0459 in relative displacement (0.0919 in double amplitude), static load 472.1 lb; 3σ up-crossings 1.125 per second, 135 in the run; level with 1 % exceedance probability in 120 s 5.29σ = 83.3 g; Davenport expected largest peak 4.47σ = 70.4 g
- Stress 0.8 ksi/g × 47.21 g = 37.77 ksi against 60 ksi: M.S. = +0.59 (limit)
Notes
The tool's default inputs are this case; press Submit. The profile rms values of GSFC-STD-7000 Tables 2.4-3 and 2.4-4, NASA-HDBK-7005 Tables 8.9 and 8.10, MIL-STD-810H Tables 514.8C-I, C-II and C-IX and Figure 514.8E-1, Irvine's PSD-integration example (8.09 GRMS) and his 500 Hz relative-displacement case (0.00068 in), the white-noise closed forms and a seeded time-domain simulation (References/Random-Vibration/checks/randresp_check.py) are checked in test_random_vibration_response.php.