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# Relationship between fatigue and vibrations

## Relationship between fatigue and vibrations

(OP)
Hello,
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

The fact that there is resonance relates to increased amplitudes (as mentioned above) and therefore increased cyclic stress, and the time to fatigue is governed by the number of load cycles: in the case of vibration fatigue life is governed by the frequency.
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

Note sure if you are looking at random vibration or sinusoidal vibration. If you are looking at sinusoidal vibe then you must take into a account damage at the frequency you are operating at (which if it is resonance will be high). If you are discussing random vibe see below:

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

The short answer to your question is yes, there is a relationship between fatigue and vibration. In fact, the stresses that originate at resonance are exploited in ultrasonic fatigue testing to reduce the explore the very high cycle regime (between 10^7 and 10^9 cycles).

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

Fatigue damage will take resonances and natural frequencies into consideration, and we often call it Vibration Fatigue Damage. If you have a loading not at the natural frequency (actually far away from the natural frequency), you will most likely only accumulate static fatigue. (No amplification as you have at resonances)

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