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Power Spectral Density Tutorials  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 P95/50 Rule -- Theory and Application   P9550.pdf Piersol, The Analysis of Nonstationary Vibration Data nonstationary_data.pdf

Sine and Random Vibration Equivalence   Sine and Random Vibration Equivalent Damage  sr_damage.pdf   Sine and Random Vibration Equivalence  sineran.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

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 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 spatial power spectral density). random_surface.pdf Methods for Converting a Power Spectral Density to a Shock Response Spectrum psd_srs.pdf

Random Vibration 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

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.	Windows version psd_syn.exe DOS version: psdgen.exe	DOS version:  psdgen.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
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
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
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