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 An Introduction to Random Vibration. A random vibration signal is analyzed in terms of its histogram, probability density function, and descriptive statistics.
 random.pdf
 Power Spectral Density Units [ G^2 / Hz ]. The bandpass filtering method is used to demonstrate a power spectral density calculation.
 psd.pdf
Integration of the Power Spectral Density Function:
The overall GRMS value is obtained by integration, for log-log format.
 psdinteg.pdf
Acceleration, Velocity, and Displacement Power Spectral Density Functions. Calculation methods are presented to convert any of these function to the other two functions.
 avdpsd.pdf  
A Method for Power Spectral Density Synthesis. The method begins with a white noise time history. The Fourier transform is then manipulated to obtain the desired power spectral density functions.
  psdsyn.pdf 
PSD synthesis example using step-by-step software program instructions.
psd_synthesis_example.pdf
Equivalent Static Load for Random Vibration. The static load is taken from the three-sigma vibration response.
 eqstatic.pdf
Power Spectral Density Calculation via Matlab:
Guest tutorial submitted by Bob Light.
 psd_mat.pdf
 Estimating the Transmissibility Q for Random Vibration
 random_Q.pdf

dB/octave Calculations for Log-Log Plots

dB_octave.pdf

Piersol, The Analysis of Nonstationary Vibration Data
nonstationary_data.pdf

Further materials for nonstationary vibration is given at:  nonstationary page

 

Tolerance Factor Tutorials

Uncertainty Margins in Aerospace Vibroacoustic Levels

This paper also includes recommendations for establishing maximum expected flight levels, as well as acceptance and qualification test levels.

uncertainty.pdf

Normal Tolerance Factors for Upper Tolerance Limits

Matlab Script: k_factor.m

normal_tolerance_factors.pdf

C. Link, An Equation for One-Sided Tolerance Limits for Normal Distributions

fplrp458.pdf

P95/50 Rule -- Theory and Application 
P9550.pdf

I. Yunis & D. Ludwiczak, On the Use of 3dB Qualification Margin for Structural Parts on ELV

yunis_3db_05.pdf

 

 Sine-on-Random Vibration

Single-degree-of-freedom System Response to Sine-on-Random Vibration
sine_on_random.pdf

A. Gokce & M. Baker, Sine on Random Analysis: Alternatives and Challenges

SORA_bhawk_tech_paper.pdf

Andrew Brown & D.S. McGhee, NASA Marshall Space Flight Center
NASA/TP-2003-212257, Statistical Evaluation and Improvement of Methods for Combining Random and Harmonic Loads,
Statistical Comparison and Improvement of Methods for Combining Random and Harmonic Loads (non-copyright AIAA paper)
combined_sine_random.pdf
AIAA-2004-1535-625.pdf
 

 Sine, Random and Shock Vibration Equivalence 

 

On the use of a Narrowband Random Power Spectral Density to Cover a Pure Sine Vibration Environment via Rainflow Fatigue

random_sine_rainflow.pdf

 Sine and Random Vibration Equivalent Damage
 sr_damage.pdf
Sine and Random Vibration Equivalence
 sineran.pdf
Extracting Sine Tones from a Power Spectral Density extract_sine_tones.pdf
 Fackler, SVM-9, Equivalence Techniques for Vibration Testing
 equiv.pdf
 A Comparison of Sine and Random Vibration via Tustin's Demonstration Device
 Tustin.pdf
Shock and Random Vibration Equivalence
shock_vib_eq.pdf
 

 Vibraton Response Spectrum

 Introduction to the Vibration Response Spectrum
 vrs.pdf 
Figure_1_psd.txt
 Derivation of Miles Equation
 Miles.pdf
 Simmons, Miles Equation
 Simmons_MilesEquation.pdf
 Enveloping Data via the Vibration Response Spectrum
 envelope.pdf

Deriving a Random Vibration Maximum Expected Level with Consideration for Kurtosis

 

envelope_kurtosis.pdf

Optimizing a Circuit Board Natural Frequency with Respect to Random Vibration.

The optimization is achieved using the vibration response spectrum.
 cb_opt_fn.pdf
The Response of a Single-Degree-of-Freedom System to Excitation from Random Surface Irregularities. (The input function may be a s patial power spectral density).
random_surface.pdf
Methods for Converting a Power Spectral Density to a Shock Response Spectrum
psd_srs.pdf
 

 Random Vibration Stress & Fatigue

 Random Vibration Fatigue:
Includes Miner's Cumulative Damage Index.
 Rfatigue.pdf
Time-Scaling Equivalence Methods for Random Vibration Testing
 tscale.pdf
A Fatigue Equivalence Method for Enveloping Nonstationary Random Vibration
enveloping_nonstationary.pdf
 Vibration Fatigue Criteria for Electrical Components
 ec_fat.pdf

Sandia Report, An Efficient Method for Calculating RMS von Mises Stress in a Random Vibration Environment

Sandia_vm_stress.pdf

Effect of Conformal Coating on Circuit Board Vibration Response
conformal_coat.pdf
 

 Random Vibration Testing

Random Vibration Band-Splitting, Martin Marietta
bandsplit.pdf
Time-Scaling Equivalence Methods for Random Vibration Testing
 tscale.pdf
Bastien, Random Vibration (Stress Screening) of Printed Wiring Assemblies
RV_SS_PWA.pdf
 

 Statistical Distributions

 The Rayleigh Distribution
 RayD.pdf
 Integration of the Normal Distribution Curve
 int_pdf.pdf
 
 Additional information regarding random vibration is given in Course Materials
 

 Software Description

 Executable

  Source

This program accepts an acceleration, velocity, or displacement power spectral density function. Given one of these functions, the program then integrates or differentiates as appropriate to find the other two functions. The program also calculates the overall level of each of the three functions.
 psdint.exe
 psdint.cpp
Synthesis of a time history to satisfy a power spectral density using white noise
 Windows version
psd_syn.exe
DOS version:

psdgen.exe
 DOS version:
 psdgen.cpp
Synthesis of a time history to satisfy a power spectral density using a sine series
psd_sine.exe psd_sine.cpp
Synthesis of a time history to satisfy a Fourier magnitude using a sine series
fourier_mag_sine.exe fourier_mag_sine.cpp
Synthesis of a time history to satisfy a sine-on-random specification
sine_on_random.exe
sine_on_random.cpp
Power spectral density of a time history signal. This program uses the FFT method. Single PSD file output.
poweri_lite.exe
poweri_lite.cpp
Power spectral density of a time history signal. This program uses the FFT method. Various output files.
 poweri.exe
 poweri.cpp
Acceleration PSD from a velocity time history, such as data from a laser vibrometer.
LV_PSD.exe
LV_PSD.cpp
Calculate a PSD via successive bandpass filtering.
filter_psd.exe
filter_psd.cpp
 Energy Spectral Density
 espec.exe
 espec.cpp
Calculations involving slopes in dB/octave. Can be used for both power spectral densities and shock response spectra.
 dboct.exe

 _

 Vibration response spectrum of a single-degree-of-freedom system subjected to base excitation.
  vrs.exe
  vrs.cpp
Conversion of a vibration response spectrum to a power spectral density.
 vrs_to_psd.exe
vrs_to_psd.cpp 
Response of an individual single-degree-of-freedom system to base excitation PSD.
 sdof_ran.exe
 sdof_ran.cpp
Response of an individual single-degree-of-freedom system to an applied force PSD.
sdof_ran_force.exe
 sdof_ran_force.cpp
Optimum envelope of a power spectral density function using the vibration response spectrum method.
 envelope.exe
envelope_rank.exe
 envelope.cpp
envelope_rank.cpp

Derive a Random Vibration Maximum Expected Level with Consideration for Kurtosis using 3-sigma VRS

envelope_kurtosis.exe

envelope_kurtosis.cpp

Derive a Random Vibration Maximum Expected Level with Consideration for Kurtosis using the n-sigma VRS method,
where n=sqrt[ 2 ln (fnT) ]

envelope_kurtosis_ns.exe

envelope_kurtosis_ns.cpp

Maximum envelope of a PSD or SRS function.
max_envelope.exe
max_envelope.cpp
Generation of a "white noise" time history.
 white.exe
 white.cpp
Circuit board fatigue via Steinberg's formula. 
 circuit_board.exe

 _

Logarithmic interpolation of a frequency domain function.
 intlog.exe
 intlog.cpp
Response PSD calculation from a power transmissibility and input PSD.
psd_transm.exe
psd_transm.cpp
Linear interpolation of a time history.
 interp.exe
 interp.cpp
The peak distribution of a time history in terms of a probability density function. The peak distribution of a narrowband process may follow a Rayleigh distribution.
 peak_dist.exe
 peak_dist.cpp
 Histogram of a time history.
 histogra.exe
 histogra.cpp
 Zero crossings of a time history.
 zero_cross.exe
  zero_cross.cpp
This program multiplies the Fourier transform of a base input function by the transfer function of a single-degree-of-freedom system.
 transfer_fft.exe
 transfer_fft.cpp

Convert a PSD with constant bandwidth to octave, one-third octave, or one-sixth octave format.

  PSDoct.exe

  PSDoct.cpp

This program transform a PSD from one resolution to another. The input PSD must have a constant spectral bandwidth.
 psd_resolution.exe
 psd_resolution.cpp
 Average PSD from individual PSD records.
psd_ave.exe 
 psd_ave.cpp
 PSD sum from individual PSD records.
psd_add_set.exe psd_add_set.cpp
Maximum PSD from individual PSD records.
 psd_max.exe 
 psd_max.cpp
This program calculates the P95/50 level of a number of PSD functions.

The P95/50 level is the 95th percentile value with a 50 percent confidence.
 psd_9550.exe
 psd_9550.cpp
Calculate magnitude versus frequency from PSD function.
 psd_magnitude.exe
  psd_magnitude.cpp

Convert a displacement PSD in dB format to a velocity RMS spectrum

disp_psd.exe

disp_psd.cpp

Sine and Random Vibration Equivalent Damage
 damage.exe
 damage.cpp
Peak SDOF response from the Rayleigh distribution
DOS
peak_response.exe
Windows
peak_response_random.exe
peak_response.cpp
Probability calculator for the following distributions:

1. Normal
2. Binomial
3. Poisson
4. Rayleigh
stats.exe

-

Unit conversion program.
units.exe
DLL files:
mfc100u.dll
msvcr100.dll

 

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