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Synthesizing a Time History to Satisfy a Power Spectral Density using Random Vibration

Unit 14. Synthesizing a Time History to Satisfy a Power Spectral Density using Random Vibration. Synthesis Purposes. A time history can be synthesized to satisfy a PSD A PSD does not have a unique time history because the PSD discards phase angle

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Synthesizing a Time History to Satisfy a Power Spectral Density using Random Vibration

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  1. Unit 14 Synthesizing a Time History to Satisfy a Power Spectral Density using Random Vibration

  2. Synthesis Purposes • A time history can be synthesized to satisfy a PSD • A PSD does not have a unique time history because the PSD discards phase angle • Vibration control computers do this for the purpose of shaker table tests • The synthesized time history can also be used for a modal transient analysis in a finite element model • This is useful for stress and fatigue calculations

  3. Random Vibration Test The Control Computer synthesizes a time history to satisfy a PSD specification.

  4. Synthesis Steps

  5. NAVMAT P-9492 PSD Overall Level = 6.06 GRMS Accel (G^2/Hz) Frequency (Hz)

  6. Time History Synthesis • vibrationdata > PSD Analysis > Acceleration PSD Time History Synthesis • Input file: navmat_spec.psd • Duration = 60 sec • sps = 16384, df = 2.44 Hz, dof = 292 • Save Acceleration time history as: input_th.txt • Save Acceleration PSD as: input_psd.txt

  7. Base Input Array: input_th.txt

  8. Base Input

  9. Base Input Array: input_psd.txt

  10. SDOF System Subject to Base Excitation NESC Academy The natural frequency is Example: fn = 200 Hz, Q=10

  11. Acceleration Response (G) max = 45.94 min = -47.21 crest factor = 4.232 mean = 5.331e-05 std dev = 11.16 rms = 11.16 skewness = -0.000856 kurtosis = 3.01 The theoretical crest factor from the Rayleigh distribution = 4.47 Array: response_th.txt

  12. Response fn=200, Q=10 The response is narrowband random. There are approximately 50 positive peaks over the 0.25 second duration, corresponding to 200 Hz.

  13. Response fn=200, Q=10

  14. SDOF Response fn=200 Hz Q=10 Rayleigh Distribution

  15. Response fn=200, Q=10 Array: response_psd.txt Peak is ~ 100 x Input at 200 Hz. Q^2 =100. Only works for SDOF system response. sps = 16384, df = 2.44 Hz, dof = 292

  16. Response fn=200, Q=10

  17. Array: trans.txt

  18. Half-power Bandwidth Points (-3 dB) • f = (208-188) Hz • = 20 Hz • Viscous Damping Ratio • = f / (2 f ) • = 20/ (2*200) • = 0.05 • Q = 1 / ( 2 * 0.05 ) • Q = 10 x: 188 y: 49 x: 208 y: 49 3 dB Bandwidth  20 Hz

  19. Half Power Bandwidth & Curve-fit Q = fn / Δf fn = natural frequency Δf = frequency bandwidth for -3 dB points Q = 200 Hz / 20 Hz = 10 Now perform a curve-fit using the parameters shown on the next slide.

  20. fn = 200 Hz damping ratio = 0.0503 Q = 9.94

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