Random Vibration

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Random Vibration & Power Spectral Density Page

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Email: tom@vibrationdata.com

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
Histogram of a time history.	histogra.exe	histogra.cpp peak_dist.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

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

Welcome to Vibrationdata Random Vibration & Power Spectral Density Page

The subscription entitles the user to download all of the items on this page, as well as other Vibrationdata pages.

Thank you for your support.

Sincerely, Tom Irvine Email: tom@vibrationdata.com

An Introduction to Random Vibration. A random vibration signal is analyzed in terms of its histogram, probability density function, and descriptive statistics.

Power Spectral Density Units [ G^2 / Hz ]. The bandpass filtering method is used to demonstrate a power spectral density calculation.

Integration of the Power Spectral Density Function: The overall GRMS value is obtained by integration, for log-log format.

Acceleration, Velocity, and Displacement Power Spectral Density Functions. Calculation methods are presented to convert any of these function to the other two functions.

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.

PSD synthesis example using step-by-step software program instructions.

Equivalent Static Load for Random Vibration. The static load is taken from the three-sigma vibration response.

Power Spectral Density Calculation via Matlab: Guest tutorial submitted by Bob Light.

Estimating the Transmissibility Q for Random Vibration

Piersol, The Analysis of Nonstationary Vibration Data

Further materials for nonstationary vibration is given at: nonstationary page

Tolerance Factor Tutorials

P95/50 Rule -- Theory and Application

Sine-on-Random Vibration

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

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)

Sine, Random and Shock Vibration Equivalence

Sine and Random Vibration Equivalent Damage

Sine and Random Vibration Equivalence

Fackler, SVM-9, Equivalence Techniques for Vibration Testing

A Comparison of Sine and Random Vibration via Tustin's Demonstration Device

Shock and Random Vibration Equivalence

Vibraton Response Spectrum

Introduction to the Vibration Response Spectrum

Derivation of Miles Equation

Simmons, Miles Equation

Enveloping Data via the Vibration Response Spectrum

Optimizing a Circuit Board Natural Frequency with Respect to Random Vibration. The optimization is achieved using the vibration response spectrum.

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).

Methods for Converting a Power Spectral Density to a Shock Response Spectrum

Random Vibration Stress & Fatigue

Random Vibration Fatigue: Includes Miner's Cumulative Damage Index.

Time-Scaling Equivalence Methods for Random Vibration Testing

A Fatigue Equivalence Method for Enveloping Nonstationary Random Vibration

Vibration Fatigue Criteria for Electrical Components

Effect of Conformal Coating on Circuit Board Vibration Response

Random Vibration Testing

Random Vibration Band-Splitting, Martin Marietta

Time-Scaling Equivalence Methods for Random Vibration Testing

Bastien, Random Vibration (Stress Screening) of Printed Wiring Assemblies

Statistical Distributions

The Rayleigh Distribution

Integration of the Normal Distribution Curve

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.

Synthesis of a time history to satisfy a power spectral density using white noise

Windows version

DOS version: psdgen.exe

DOS version: psdgen.cpp

Synthesis of a time history to satisfy a power spectral density using a sine series

Synthesis of a time history to satisfy a Fourier magnitude using a sine series

Synthesis of a time history to satisfy a sine-on-random specification

Power spectral density of a time history signal. This program uses the FFT method. Single PSD file output.

Power spectral density of a time history signal. This program uses the FFT method. Various output files.

Acceleration PSD from a velocity time history, such as data from a laser vibrometer.

Calculate a PSD via successive bandpass filtering.

Energy Spectral Density

Calculations involving slopes in dB/octave. Can be used for both power spectral densities and shock response spectra.

Vibration response spectrum of a single-degree-of-freedom system subjected to base excitation.

Conversion of a vibration response spectrum to a power spectral density.

Response of an individual single-degree-of-freedom system to base excitation PSD.

Response of an individual single-degree-of-freedom system to an applied force PSD.

Optimum envelope of a power spectral density function using the vibration response spectrum method.

Maximum envelope of a PSD or SRS function.

Welcome to Vibrationdata
Random Vibration & Power Spectral Density Page

Sincerely, Tom Irvine
Email: tom@vibrationdata.com

Integration of the Power Spectral Density Function:
The overall GRMS value is obtained by integration, for log-log format.

Power Spectral Density Calculation via Matlab:
Guest tutorial submitted by Bob Light.

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

The optimization is achieved using the vibration response spectrum.

Random Vibration Fatigue:
Includes Miner's Cumulative Damage Index.

DOS version:

psdgen.exe

DOS version:
psdgen.cpp