# SN diagram vs. Cycle Frequency

1. Mar 26, 2017

### Simas

Hi,

What is the effect of the load cycle frequency on the SN curve (Wöhler curve)? Especially when the frequency matches the natural frequency of the component/material?

Instinctively, I would think that at the natural frequency the number of load cycles until fracture is lower than at any other frequency due to increase of amplitude at resonance. But I do not understand how you can see/show this in the SN curve.

Thank you,
Simas

2. Mar 26, 2017

### JBA

Unfortunately, as a component forced frequency approaches it natural frequency it transforms to a realm known as "low cycle fatigue" which is the reason that the S/N curve is specified for "high cycle fatigue". For more information on this issue do a web search for "low cycle fatigue" and you will find a large volume on the subject.

3. Apr 6, 2017

### Dr.D

As you approach the natural frequency of a dynamic system, the system response typically increases rather drastically. This causes stress fluctuations that are far larger than those occurring for well-off natural frequency response.

4. Apr 7, 2017

### Simas

For example, a typical cantilever beam as on the picture below, the bending stress in point B due to a cyclic force P is calculated as M(L)*y/I, with M(L) the bending moment in B (= P*L), y the height/2, and I the inertia moment. But this formula for the stress does not take into account the resonance effect, because according to this formula, the stress amplitude is the same for all frequencies. How do I take the resonance effect (drastic increase of the stress at natural frequency) into account?

5. Apr 7, 2017

### Dr.D

I would suggest that you start with a vibration model based on distributed mass (distributed along the length of the beam). Obtain a solution for the dynamic deflection as a function of time and location. Then calculate the bending stress as Mc/I at point B.

The standard SN curves do not apply, so you are really flying blind at this point. I suggest that you apply a conservative failure criterion and see if it appears that cracks will propagate. If you want to get into more detail, research "fracture mechanics."

This is not a problem for amateurs!