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

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Presentation transcript:

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 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

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

Synthesis Steps Step Description 1 Generate a white noise time history 2 Take the FFT 3 Scale the FFT amplitude per the PSD for each frequency 4 The time history is the inverse FFT 5 Use integration, polynomial trend removal, and differentiation so that corresponding mean velocity and mean displacement are both zero 6 Scale the time history so that its GRMS value matches the specification’s overall GRMS value 7 Take a PSD of the synthesized time history to verify that it matches the PSD specification

PSD Overall Level = 6.06 GRMS NAVMAT P-9492 PSD Overall Level = 6.06 GRMS Accel (G^2/Hz) Frequency (Hz) Accel (G^2/Hz) 20 0.01 80 0.04 350 2000 0.007 Frequency (Hz)

Time History Synthesis vibrationdata > Power Spectral Density > Time History Synthesis from White Noise Input file: navmat_spec.psd Duration = 60 sec Row 8, df = 2.13 Hz, dof = 256 Save Acceleration time history as: input_th Save Acceleration PSD as: input_psd

Base Input Matlab array: input_th

Base Input

Base Input Matlab array: input_psd

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

Matlab array: response_th Acceleration Response (G) max= 52.69 min= -52.56 RMS= 11.24 crest factor= 4.69 Relative Displacement (in) max= 0.01279 min=-0.01282 RMS=0.002735 The theoretical crest factor from the Rayleigh distribution = 4.58 Matlab array: response_th

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.

Response fn=200, Q=10

PSD SDOF Response fn=200 Hz Q=10 Rayleigh Distribution

Matlab array: response_psd Response fn=200, Q=10 Matlab array: response_psd Row 8, df = 2.13 Hz, dof = 254 Peak is ~ 100 x Input at 200 Hz. Q^2 =100. Only works for SDOF system response.

Response fn=200, Q=10

Matlab array: trans

3 dB Bandwidth  20 Hz

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.