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## Fatigue Damage for a Stress Response PSD

Here is a paper.

Estimating Fatigue Damage from Stress Power Spectral Density Functions: estimate_fatigue_psd.pdf

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This following Matlab program calculates the cumulative rainflow fatigue damage for an input stress PSD using the following wideband methods:

1. Wirsching & Light
2. Ortiz & Chen
3. Lutes & Larsen, Single-Moment
4. Benasciutti & Tovo, alpha 0.75
5. Dirlik
6. Zhao & Baker

Reference:

The stress PSD and the fatigue strength coefficient must have consistent stress units.

The input PSD must have two columns: freq(Hz) & stress(unit^2/Hz)

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Main scripts:

stress_psd_fatigue.zip

Vibrationdata Signal Analysis Package

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The following values are “For Reference Only.”

m = fatigue exponent
A = fatigue strength coefficient

Aluminum 6061-T6 with zero mean stress

m=9.25
A=9.7724e+17 (ksi^9.25)
A=5.5757e+25 (MPa^9.25)

Butt-welded Steel Joints

m=3.5
A=1.255e+11 (ksi^3.5)
A=1.080e+14 (MPa^3.5)

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Rainflow Fatigue

Mrsnik, Janko Slavic, Boltezar, Frequency-domain methods for a vibration-fatigue-life estimation – Application to real data:  mrsnik_article_vib_fatigue.pdf

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- Tom Irvine

## Webinar 16 – Vibration Response Spectrum

PowerPoint File:

Webinar_16_VRS.pptx

Audio/Visual File:

VRS.wmv

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Python Version

Webinar_16_VRS_python.pptx

Python script: Python Signal Analysis Package GUI

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PSD Data Files:

webinar_16_data_files.mat

webinar_16_data_files.zip

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Reference Paper:

An Introduction to the Vibration Response Spectrum link

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Matlab script:  Vibrationdata Signal Analysis Package

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- Tom Irvine

## Webinar 15 – SDOF Response to Base Input in the Frequency Domain

PowerPoint File:

webinar_15_SDOF_frequency_domain.ppt

Audio/Visual File:

SDOF_response_base_input_frequency_domain.wmv

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PSD Data File:

navmat_spec.psd

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Python

webinar_15_SDOF_frequency_domain_python.pptx

Python script: Python Signal Analysis Package GUI

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Reference Papers:

The Steady-state Response of Single-degree-of-freedom System to a Harmonic Base Excitation link

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Matlab script: Vibrationdata Signal Analysis Package

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- Tom Irvine

## Fatigue Damage Spectrum, Frequency Domain

There is an occasional need to compare the effects of two different power spectral density (PSD) base input functions for a particular component. This would be the case if the component has already been tested to one PSD but now must be subjected to a new PSD specification.

A comparison can readily be performed using a Vibration Response Spectrum (VRS) if the PSDs have the same duration. This requires estimates of the bounds for both the amplification factor Q and the natural frequency.

The task is more complex if the PSDs have different durations. A Fatigue Damage Spectrum (FDS) comparison can be performed as an extension of the VRS method. This also requires estimates of the fatigue exponent.

The method is demonstrated using an actual case history: psd_fatigue_comparison.pdf

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Here is the source code for a C++ vibration response program which has a fatigue damage spectrum option: vrs.cpp

The calculation can also be performed using:

Matlab script: Vibrationdata Signal Analysis Package

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Rainflow Fatigue Cycle Counting

Dirlik Rainflow Counting Method from Response PSD

SDOF Response to an acceleration PSD Base Input

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- Tom Irvine

## Webinar 14 – Synthesizing a Time History to Satisfy a PSD Specification

PowerPoint File:

Webinar_14_PSD_synthesis.pptx

Audio/Visual File:

PSD_synthesis.wmv

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PSD Data File:

navmat_spec.psd

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Matlab script: Vibrationdata Signal Analysis Package

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Python Version

Webinar_14_PSD_synthesis_python.pptx

Python script: Python Signal Analysis Package GUI

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- Tom Irvine

## Webinar 13 – SDOF Response to Power Spectral Density Base Input

PowerPoint File:

Webinar_13_PSD_sdof_response.pptx

Audio/Visual File:

SDOF_Response_to_PSD_Input.wmv

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Reference Paper:  Derivation of Miles Equation

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Matlab script: Vibrationdata Signal Analysis Package

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Python Version: Webinar_13_PSD_sdof_response_python.ppt

Python script: Python Signal Analysis Package GUI

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- Tom Irvine

## Webinar 12 – Power Spectral Density Functions of Measured Data

PowerPoint File:

Webinar_12_PSD_data.pptx

Audio/Visual File:

PSD data.wmv

Data:

Taurus_auto.dat – Time(sec) & Accel(G)

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Matlab script: Vibrationdata Signal Analysis Package

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Python Version:  Webinar_12_PSD_data_python.pptx

Python script: Python Signal Analysis Package GUI

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