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 14  Enveloping Nonstationary Vibration via Fatigue Damage Spectra

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, Variable Amplitude Loading

Unit 26  Airbus Fatigue Manual

More later…

– Tom Irvine

Waterfall SRS, 1940 El Centro Quake



The top figure is the time history from the El Centro earthquake, North-South horizontal component.  The second is the corresponding Waterfall FFT with 4 second segments and with 50% overlap.

The Waterfall FFT is calculated by first taking the complete response time history for each natural frequency of interest.  Then the time history for each is divided into segments.  Finally, the shock response spectrum (SRS) is taken for each natural frequency and for each segment, by taking the peak positive and peak negative responses.

The Waterfall SRS function is given in:

Matlab script: Vibrationdata Signal Analysis Package

>> vibrationdata > Time History > Shock Response Spectrum, Various > Waterfall FFT

See also:  El Centro Earthquake

– Tom Irvine

Tom’s Video & Animation Files

Another work-in-progress…

Step 1: Download a video file.
Step 2: Play using VLC media player.

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Launch Vehicles

Delta 4 Heavy Launch Vehicle Shock Events

Pegasus Launch Vehicle

Linear Shaped Charge Test

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Chinook Ground Resonance

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Fixed Wing Aircraft

MD80 Tail Failure

Boeing 747 Wind Tunnel

C-5 Tail Wind Tunnel

Twin Commanche

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Automotive & Transportation

Triple Trailer Oscillation

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Shock & Vibration Testing

Generator Seismic Shaker Test

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Fluid Systems

Pool Slosh 1

Pool Slosh 2

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Half-Sine SRS Animation

Multi-axis Shock & Vibration Testing

Equipment must be designed and tested to withstand shock and vibration.  Ideally, all equipment would be tested on a shaker table with six-degree-of-freedom control (three translations and three rotations).  Such tables and control systems exist but are very expensive.  Furthermore, any multi-axis testing requires careful consideration of phase angles between the six degrees.

Another option is to test equipment on a triaxial table where the three translations are controlled, and the three rotational degrees are constrained to zero motion.  Testing on a biaxial table is yet another choice.

The most common test method, however, remains testing in each of three orthogonal axes, one axis at a time, on a single-axis shaker.  This is simplest and least expensive method.

The question arises “Should the acceleration level be increased for the case of single-axis testing?”

There is a tacit understanding that aerospace and military equipment test levels already have a sufficient uncertainty margin or safety factor so that the levels can be used without further increase.  In other words, the specifications are already intended for single-axis testing.  In many cases, a uniform level is used in each axis which is the maximum envelope of the maximum expected levels in the three axes plus some margin.

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The standards which address testing equipment for earthquakes take a different approach. The following descriptions are taken from five common standards.

Only KTA 2201.4 gives a scaling formula.  This is also the only standard from the five samples which may be freely downloaded.

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IEEE 344-2013  Standard for Seismic Qualification of Equipment for Nuclear Power Generating Stations

8.6.6 Multiaxis tests

Seismic ground motion occurs simultaneously in all directions in a random fashion. However, for test purposes, single-axis, biaxial, and triaxial tests are allowed. If single-axis or biaxial tests are used to simulate the 3D environment, they should be applied in a conservative manner to account for the absence of input motion in the other orthogonal direction(s). One factor to be considered is the 3D characteristics of the input motion. Other factors are the dynamic characteristics of the equipment, flexible or rigid, and the
degree of spatial cross-coupling response. Single and biaxial tests should be applied to produce adequate levels of excitation to equipment where cross coupling is significant and yet minimize the level of overtesting where the cross coupling is not significant.

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KTA 2201.4   Design of Nuclear Power Plants against Seismic Events, Part 4: Components

This document may be freely downloaded: link

See paragraphs

5.3.3 Excitation Axes Simultaneity of excitation directions

Simultaneous three-axis testing is preferred. But single-axis testing can be substituted by testing in each of three axes sequentially.

The standard shows, for example, that the uniform single-axis level should be the “square root of the sum of the squares” of the three orthogonal installation site levels.

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IEC 980 Recommended practices for seismic qualification of electrical equipment of the safety system for nuclear generating stations

6.2.9 Qualification test method General

As is well known, seismic excitation occurs simultaneously in all directions in a random way. According to this point of view, the test input motion should consist of three mutually independent waveforms applied simultaneously along the three orthogonal axes of the equipment.

However, taking into account that three axial testing installations are rare and that triaxial testing is desirable when significant coupling exists simultaneously between the two preferred horizontal axis of the specimens, biaxial testing with multifrequency independent input motion in the horizontal and vertical direction is an acceptable test.

Tests shall be performed according to 6.3.2 and, in terms of total duration and fatigue induced, are intended to become conservative.

In some cases, single axis tests with multiple, or single frequency excitation are also acceptable methods of test if properly justified considering the effect of coupling between axes.

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Telcordia GR-63-CORE

Assumes single-axis testing.  The base input time history is specified in the standard.

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IEEE 693-2005 – IEEE Recommended Practice for Seismic Design of Substations

paragraph 4.9

The shaker table shall be biaxial with triaxial preferred.

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See also:

Seismic Test & Analysis Webinars

Hypersphere SRS


– Tom Irvine

Webinar Index

Here is a listing of the webinars and related materials.

Matlab script: Vibrationdata Signal Analysis Package

1. Natural Frequencies

2. Sine Vibration

3. Sine Sweep Vibration

4. Random Vibration

5. Fourier transforms

6. Leakage Error, Hanning Window

7. FFTs

8. Waterfall FFT

9. White Noise FFT

10. Sample Rate & Aliasing

11. Power Spectral Density

12. Power Spectral Density Functions of Measured Data

13. SDOF Response to Power Spectral Density Base Input

14. Synthesizing a Time History to Satisfy a PSD Specification

15. SDOF Response to Base Input in the Frequency Domain

16. Vibration Response Spectrum

17. SDOF Response to Applied Force

18. Force Vibration Response Spectrum

19. Digital Filtering

20. Digital Filtering, Part 2

21. Integration & Differentiation of Time Histories

22. Integration and Differentiation of Time Histories & Spectral Functions

23. Classical Shock Pulse

24. Seismic Shock

25. Pyrotechnic Shock

26. Pyrotechnic Shock, part 2

27. SRS Synthesis

28. Multi-degree-of-freedom SRS

29. Stress-Velocity Relationship

30. Rectangular Plate Shock & Vibration

31. Rectangular & Circular Plate Shock & Vibration

32. Electronic Circuit Board Fatigue

33. Rainflow Fatigue

34. Rainflow Fatigue for Continuous Beams

35. Using Fatigue to Compare Sine and Random Environments

36. Non-Gaussian Random Fatigue and Peak Response

37. Acoustic Fatigue

38. Electronic Circuit Board Fatigue Part 2

39. Sine-on-Random Vibration

40. Shock Fatigue

41. PSD Special Topics

42. Shock Special Topics

43. Two-degree-of-freedom System, Two-stage Isolation

44. Sine Filtering

45. Two-degree-of-freedom System with Rotation and Translation

46. Two-degree-of-freedom System with Multi-point Enforced Motion

47. Shock Response Spectrum Synthesis, Special Topics

Seismic Test & Analysis Webinars

Structural Dynamics Webinars

Fatigue Webinars

Circuit Board Shock & Vibration Analysis

HALT/HASS for Product Reliability

More later. . .

– Tom Irvine

Seismic Test & Analysis Webinars

This is a work-in-progress…

I am creating a series of webinars with Matlab exercises for seismic testing.

Here are the slides.

Telcordia Technologies Generic Requirements GR-63-CORE:  Bellcore_GR_63_Core.ppt
This unit contains an alternative waveform for VERTEQII.

CEI.IEC 980, Recommended practices for seismic qualification of electrical equipment of the safety system for nuclear generating stations:  CEI/IEC 980: 1989

IEEE Std 693-2005, Recommended Practice for Seismic Design of Substations: IEEE_693_sine_beat.pptx

IEEE Standard for Seismic Qualification of Equipment for Nuclear Power Generating
Stations: IEEE_std_344.ppt

Matlab script: Vibrationdata Signal Analysis Package

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See also:

Cummins Generator Seismic Shaker Test

Earthquake Conference

Seismic Shock

Webinar 47 – Shock Response Spectrum Synthesis, Special Topics

Seismic Peak Ground Acceleration

Some Earthquake Engineering Terminology

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– Tom Irvine

Shock & Vibration Courses, Trieste, Italy & Singapore

You are welcome to participate in any of the following courses.

I will teach shock & vibration course in Trieste, Italy on January 25-27, 2017.   Course Link

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I will teach a shock & vibration finite element analysis course in Singapore, February 13-15, 2017.  Brochure Link

Thank you,
Tom Irvine

Structural Dynamics Webinars

This is a work-in-progress…

I am creating a series of webinars with Matlab exercises for structural dynamics and finite element analysis.

Here are the slides:

Unit 1  Basic FEA

Unit 2  Damping

Unit 3 Modal Analysis

Unit 4 Transfer Functions

Unit 5  Transient Analysis

Unit 6  Applied Force Response Analysis

Unit 7  Response to Seismic Base Mass Excitation

Unit 8  Response to Enforced Motion

Unit 9  Beam Bending FEA

Unit 10 Beam Bending FEA with Added Mass and Stiffness

Unit 11 Beam Bending FEA with Steady-State Sinusoidal Base Excitation

Unit 12 Beam Bending FEA with Sine Sweep Base Excitation

Unit 13  Beam Bending FEA with PSD Base Excitation

Unit 14  Beam Bending FEA Fatigue

Unit 15  Beam Bending FEA Shock

Unit 17  FEA: Circuit Board Natural Frequencies

Unit 18  FEA: Circuit Board Damping

Unit 19  FEA: Circuit Board Response to Sine Vibration

Unit 20  FEA:  Circuit Board Response to Sine Sweep Vibration

Unit 21  FEA:  Circuit Board Response to Random Vibration

Unit 22  FEA:  Circuit Board Response to PSD Synthesis

Unit 23_FEA:  Circuit Board Shock Response Spectra & Synthesis 

Unit 24_FEA:  Circuit Board MDOF Shock

Unit 25:  FEA:  Circuit Board Fatigue

Special Topic:  Irvine_multiaxis_fatigue.pptx

Matlab script: Vibrationdata Signal Analysis Package

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See also:

Transfer Functions from Normal Modes

Convert Modal Damping to a Damping Coefficient Matrix

Beam Bending, Finite Element Analysis

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– Tom Irvine

A320 Takeoff Vibration


Figure 1.  A320 Takeoff

I recently flew as a passenger in an A320 similar to the aircraft shown in Figure 1.



Figure 2.  Time History Plots

The takeoff vibration is shown in Figure 2 for the lateral and vertical axes.   The aircraft went airborne at 393 seconds.  The fore-aft axis is omitted since its level was lower.  The sensor was a Slam Stick X mounted on the cabin floor.


Figure 3.  PSD, Lateral Axis


Figure 4.  PSD, Vertical Axis

The PSD plots show some distinct spectral peaks which are most likely forcing frequencies, or possibly lightly-damped structural resonances.

Here is the time history data file:  takeoff_data

– Tom Irvine

LDS V-8900 Shaker Table


Years ago, I had the opportunity to perform hands-on shaker table testing, mostly for avionics components.  That was a great learning experience.  Alas, that opportunity has gone, but I am still involved writing software and providing training for test engineers.

LDS was one of the shaker manufacturers during my testing days.  LDS has since merged with Bruel & Kjaer.

I met my colleague Joel Leifer at an engineering conference recently.  He informed me about a new LDS shaker model, which has a 4 inch displacement stroke.  This would be very useful for low frequency shock and vibration tests.  Videos and further information is given at:  Video Link

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Joel wrote:

I am interested in working with the space community as they define test requirements as this could be the tool they have been looking for to do some of the harder tests. Any advice or guidance you could give will be greatly appreciated.

Thanks for your attention to this.


Joel Leifer, PE
District Manager (Western Region) VTS
Bruel & Kjaer North America
8566 Van Ness Ct Unit 24F
Huntington Beach, CA 92646
Direct: 817 475-2329

So please contact Joel if you are interested in collaboration, etc.

I was going to ask Joel to provide a demo model for me so that I could do some science projects at my home, but my wife would never let me keep a shaker table in our garage :)

– Tom Irvine