## Relationship between fatigue and vibrations

## Relationship between fatigue and vibrations

(OP)

Hello,

I'm posting this thread to ask about the Relationship between fatigue and vibrations.

I know that to characterize failure due to fatigue one needs to calculate the accumulative damage, that is the sum of damages done by each cycle independantly ( each cycle is determined by its frequency, it's amplitude and mean value for sinusoidal loadings.

I also know that if a structure or a part is subjected to loads oscillating at it's natural frequency, we get what's called resonance. This leads to increasing deformations and thus failure.

What i'm having a problem with is that fatigue damage does not take into consideration ( and correct me if i'm wrong) the resonance and natural frequencies, so how can one determine the cause of failure ( fatigue or resonance) ? are fatigue and vibrations independant notions ? if not what is the relationship between them ?

I'm posting this thread to ask about the Relationship between fatigue and vibrations.

I know that to characterize failure due to fatigue one needs to calculate the accumulative damage, that is the sum of damages done by each cycle independantly ( each cycle is determined by its frequency, it's amplitude and mean value for sinusoidal loadings.

I also know that if a structure or a part is subjected to loads oscillating at it's natural frequency, we get what's called resonance. This leads to increasing deformations and thus failure.

What i'm having a problem with is that fatigue damage does not take into consideration ( and correct me if i'm wrong) the resonance and natural frequencies, so how can one determine the cause of failure ( fatigue or resonance) ? are fatigue and vibrations independant notions ? if not what is the relationship between them ?

## RE: Relationship between fatigue and vibrations

Cheers

Greg Locock

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## RE: Relationship between fatigue and vibrations

A nice example is the occurence of a torsional fatigue failure in a crankshaft of a combustion engine. At resonance speed and with a defective torsional vibration damper, life span of the crankshaft is days or weeks, no more, due to the relatively high frequency of the natural frequency of a crankshaft.

## RE: Relationship between fatigue and vibrations

What you might be looking for is using Mile's Equation combined with Miner's Rule which allows a method of damage prediction in a random vibration environment. (https://femci.gsfc.nasa.gov/workshop/2001/posters/...)

You are correct in that we typically assume that nearly all the damage during random vibration will occur due to resonance excitation. From a Power Spectral Density curve describing a random vibration environment we can use Mile's Equation to estimate the statistical 1-sigma, 2-sigma and 3-sigma peak acceleration due to resonance. We then assume these different 1-sigma, 2-sigma, and 3-sigma levels have a von mises distribution (1-sigma=68%,2-sigma=27%,3-sigma=4%)and use these levels and occurrences with miner's rule to estimate damage.

## RE: Relationship between fatigue and vibrations

As a dividing line, if the cyclic event is mainly deterministic it is treated in the time domain; if instead the stochastic component is predominant, then the validation of the part is based on vibration testing (i.e. in the frequency domain).

If you want to go deeper this topic, you'll soon realise that there is a lot of knowledge available. You may find useful to consult the following references:

- MIL-STD-810G

- "Mechanical Vibration and Shock Analysis, vol. 4: Fatigue Damage" by Christian Lalanne

- nCode online webinars (e.g. this)

## RE: Relationship between fatigue and vibrations