Fatigue Analysis Webinars


This is a work-in-progress…

I am creating a series of webinars with Matlab exercises for fatigue analysis

Matlab script: Vibrationdata Signal Analysis Package

Here are the slides:

Unit 1  Fatigue Introduction

Unit 2  Fracture

Unit 3  Sine Vibration

Unit 4  Random Vibration

Unit 5  Rainflow Cycle Counting, Time Domain

Unit 6  Sine Sweep Vibration

Unit 7   Synthesizing a Time History to Satisfy a PSD Specification

Unit 8  Drop & Classical Shock  & Video Half-Sine SRS Animation

Unit 9  Seismic & Pyrotechnic Shock & Video Delta 4 Shock Events

Unit 10  SRS Synthesis

Unit 11  Vibration Response Spectrum

Unit 12  Rainflow Fatigue, Spectral Methods, Fatigue Damage Spectrum

Unit 13  Modifying Spectral Fatigue Methods for S-N Curves with MIL-HDBK-5J Coefficients

Unit 14a  Enveloping Nonstationary Vibration via Fatigue Damage Spectra

Unit 14b  Enveloping Nonstationary Vibration, Batch Mode for Multiple Inputs

Unit 15  Using Fatigue to Compare Sine and Random Environments

Unit 16  Sine-on-random Conversion to a PSD via Fatigue Damage Spectra

Unit 17  Non-Gaussian Random Fatigue and Peak Response

Unit 18   Acoustic Fatigue

Unit 19  Shock Fatigue

Unit 20  Fatigue Damage including Mean Stress

Unit 21  Electronic Circuit Board Fatigue, Part 1

Unit 22  Electronic Circuit Board Fatigue, Part 2

Unit 23  Time-Level Equivalence

Unit 24  Multiaxis Fatigue, Constant Amplitude Loading

Unit 25  Multiaxis Fatigue, Stress Ratio Methods

Unit 26  Multiaxis Fatigue, Variable Amplitude Loading

Unit 27  Airbus Fatigue Manual

More later…

– Tom Irvine

Tom’s Conference Papers & Slide Index

I am trying to collect all my presentations. This is a work-in-progress…

Thank you,
Tom Irvine

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NAFEMS World Congress 2017

Introduction to Vibration

Spectral Functions

Random Vibration

Vibration Fatigue

Shock 1 & 2


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Aerospace Spacecraft & Launch Vehicle Dynamic Environments Conference

2017, Statistical Energy Analysis Software & Training Materials, Part 2

2016, Statistical Energy Analysis Software & Training Materials

2015, Seismic Analysis and Testing of Launch Vehicles and Equipment using Historical Strong Motion Data Scaled to Satisfy Shock Response Spectra Specifications

2014, Optimized PSD Envelope for Nonstationary Vibration

2013, Extending Steinberg’s Fatigue Analysis of Electronics Equipment to a Full Relative Displacement vs. Cycles Curve

2012,  Keynote, Dynamics Engineering: A Call to Serve  

2012, An Alternate Damage Potential Method for Enveloping Nonstationary Random Vibration

2011, The NASA Engineering & Safety Center (NESC) Shock & Vibration Training Program

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European Space Agency


ESA Pyrotechnic Shock Distance & Joint Attenuation via Wave Propagation Analysis

ESA Shock Analysis of Launch Vehicle Equipment using Historical Accelerometer Records to Satisfy Shock Response Spectra Specifications 

2016, European Conference on Spacecraft Structures Materials and Environmental Testing

Modifying Spectral Fatigue Methods for S-N Curves with MIL-HDBK-5J Coefficients

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Various Vibration & Fatigue Conferences

VAL2015, A review of spectral methods for variable amplitude fatigue prediction and new results

VAL 2015, Using a Random Vibration Test Specification to Cover a Shock Requirement via a Pseudo Velocity Fatigue Damage Spectrum

ICoEV 2015, International Conference on Engineering Vibration, Derivation of Equivalent Power Spectral Density Specifications for Swept Sine-on-Random Environments via Fatigue Damage Spectra

MOVIC & RASD 2016, Multiaxis Fatigue Method for Nonstationary Vibration

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Shock and Vibration Exchange (formerly SAVIAC)

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Institute of Environmental Sciences and Technology (IEST)

IESTECH 2016, Nonstationary Vibration Enveloping Method Comparison

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Earthquake Engineering Conferences

16th WCEE, Seismic Analysis and Testing of Equipment using Historical Strong Motion Data Scaled to Satisfy Shock Response Spectra Specifications

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2003, A Time Domain, Curve-Fitting Method for Accelerometer Data Analysis

2003, Practical Application of the Rayleigh-Ritz Method to Verify Launch Vehicle Bending Modes

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Nonstationary Vibration Enveloping Method Comparison

There is a need to derive a power spectral density (PSD) envelope for nonstationary acceleration time histories, including launch vehicle data, so that components can be designed and tested accordingly.

Three methods are considered in the following paper using an actual flight accelerometer record.

The first method divides the accelerometer data into segments which are idealized as “piecewise stationary” in terms of their respective PSDs. A maximum envelope is then drawn for the superposition of segment PSDs. This method initially requires no assumptions about the response characteristics of the test item, but vibration response spectra may used for peak clipping as shown in the example.

The following two methods apply the time history as a base input to a single-degree-of-freedom system with variable natural frequency and amplification factors. The response of each system is then calculated. Upper and lower estimates of the amplification factor can be used to cover uncertainty.

The first of this pair is the energy response spectrum (ERS), which gives energy/mass vs. natural frequency, as calculated from the relative response parameters.

The final method is the fatigue damage spectrum (FDS), which gives a Miners-type relative fatigue damage index vs. natural frequency based on the response and an assumed fatigue exponent, or upper and lower estimates of the exponent.

The enveloping for each of the response spectra methods is then justified using a comparison of candidate PSD spectra with the measured time history spectra. The PSD envelope can be optimized by choosing the one with the least overall level which still envelops the accelerometer data spectra, or which minimizes the response spectra error.

This paper presents the results of the three methods for an actual flight accelerometer record. Guidelines are given for the application of each method to nonstationary data. The method can be extended to other scenarios, including transportation vibration.

Paper:  enveloping_comparison.pdf

Slides:  Irvine_IEST_2016.pptx

The Matlab scripts for the enveloping methods are included in  Vibrationdata GUI package

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See also:

Rainflow Cycle Counting

Energy Response Spectrum

Dirlik Rainflow Counting Method from Response PSD

Fatigue Damage Spectrum, Frequency Domain

Optimized PSD for Nonstationary Vibration Environments

– Tom Irvine

Optimized PSD Envelope for Multiple Accelerometer Time Histories

Prerequisite Reference Papers

David O. Smallwood, An Improved Recursive Formula for Calculating Shock Response Spectra, Shock and Vibration Bulletin, No. 51, May 1981.  DS_SRS1.pdf

Rainflow Counting Tutorial

Fatigue Damage Spectrum, Time Domain

Fatigue Damage Spectrum

Dirlik Method for PSDs

Optimized PSD FDS Nonstationary 

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Main Paper

Consider a component mounted on a structure where the base input is measured by an adjacent accelerometer on the structure. An envelope power spectral density (PSD) is needed so that component design and test levels can be derived, with the appropriate added statistical uncertainty margin.

Assume that the base input has been measured over a series of accelerometer time histories. This could be the case for an automobile driven at different speeds over different road conditions, for example.

The envelope PSD can be derived using fatigue damage spectra as shown in:  FDS_PSD_multiple.pdf

The C++ programs are:


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Here is an alternate program that allows for repetition for a given time history file.  This is useful, for example, if a short time duration was measured to represent a longer service duration.


Now assume that there are three measured acceleration time histories where the repetition number is 10, 50 and 100, respectively.

The input file format would be:

time_history_1.txt 10
time_history_2.txt 50
time_history_3.txt 100

Substitute your own file names and multipliers accordingly.

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– Tom Irvine

Fatigue Damage including Mean Stress

Options for including mean stress have been added to the Vibrationdata GUI package’s Fatigue Toolbox, for both stress time histories and PSDs.

Four methods are available:


Matlab script: Vibrationdata Signal Analysis Package

Here are some charts from Iowa State University: Fatigue Mean Stress

– Tom Irvine

NASGRO Coefficients

The following scripts calculate the A, B, C, P coefficients to model a set of SN curves with varying R values: sin_curve_fit_R.zip

sn_curve_fit_R.m is the main script.

The remaining scripts are supporting functions.

The equations are given in: sn_curvefit_equation.pdf

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– Tom Irvine

Webinar 37 – Acoustic Fatigue

PowerPoint Slides:  webinar_37_acoustic_fatigue.pptx

Audio/Visual File:

NESC Academy Acoustic Fatigue – Recommend viewing in Firefox with Sliverlight Plugin

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Rainflow Fatigue Posts

Acoustic Fatigue of a Plate

Acoustic Power Spectra

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Matlab script: Vibrationdata Signal Analysis Package

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See also: Vibrationdata Webinars

Thank you,

Tom Irvine

Low Risk Parts for Spaceflight

NASA-STD-5019, Fracture Control Requirement for Spaceflight Hardware (excerpt) Low-Risk Part

This section addresses parts that can be classified non-fracture critical because of large structural margins and other considerations that make failure from a pre-existing flaw extremely unlikely.

a. For a part to be classified low risk, it shall be constructed from a commercially available material procured to an aerospace standard or equivalent.

b. Aluminum parts shall not be loaded in the short transverse direction if this dimension is greater than 7.62 cm (3 in).

c. A part whose failure directly results in a catastrophic hazard shall be excluded from being classified low risk, except when the total (unconcentrated) stresses in the part at limit load are less than 30 percent of the ultimate strength for the material used and requirements (1) through (3) and either (4) or (5) are met.

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Thus fatigue and fracture analyses are not required for parts with peak stress less than 0.3*ultimate.

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The peak stress can also be compared to the endurance limit, but some materials do not have identified endurance limits.  Here is a rule-of-thumb for these cases from NASA-HDBK-5010.

Perform endurance limit analysis to show the maximum stress does not exceed the endurance limit or

Smax < Ftu/( 4{1-0.5 R} )


Smax is the local concentrated stress
Ftu is the tensile ultimate stress
R is the ratio of minimum stress to maximum stress in a fatigue cycle

Note that R=-1 for fully reversed stress with zero mean stress.  For this case:  Smax < Ftu/6

This formula has some limitations and needs further research.

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– Tom Irvine

SDOF Response to Sine or Sine Sweep Base Input, Rainflow


Rainflow fatigue cycles can be easily calculated for a single-degree-of-freedom subjected to a sine or sine sweep base input.  The reason is that each pair of consecutive positive and negative response peaks forms a half-cycle.

The relative fatigue damage can then be calculated from the rainflow cycles.

Here are Matlab scripts for performing the rainflow and damage calculations.  rainflow_sine.zip

rainflow_sine.m is for the case where the natural frequency is known.

rainflow_sine_fds.m gives the fatigue damage spectrum for a family of natural frequencies.

The remaining scripts are supporting functions.

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See also:

Rainflow Cycle Counting


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– Tom Irvine