Imagine that there is a component/structure that is subjected to one harmonic load with frequency Wloading and that I would like to make an assessment of fatigue life of it. Let's consider the load as F(t)= Lmax*sin(Wloading*t).
And imagine that the 1st natural frequency of this component/structure is Wn,1st in such a way that
Wloading = 0.25 * Wn,1st
I think the most accurate way to assess the fatigue life is to do a (linear) transient analysis using FEA (for example using the Superposition Method considering 4 or more modes). Then, use the stresses along the time-history to assess the fatigue life, using rainflow counting, correction of mean stress and Palmgren-Miner.
Although, I would like to know if it is possible to do a static analysis instead of a transient one, because Wloading is relative lower than the Wn,1st. So, I thought that I could do a static analysis appling the load Lmax in the component (in the same place and direction of the force F(t) ) and would obtain the displacements and stresses in the whole component. After that, I would calculate the Amplification Factor "AF" using the equation for 1 DOF system that is:
AF = 1/sqrt( (1-(Wloading/Wn,1st)2)2 + (2*zeta*Wloading/Wn,1st)2 )
Where AF > 1 and let's consider zeta=0.03
So, I would multiply the component displacements and the component stresses by AF.
So, will be these displacements and stresses (already amplified by AF), calculated by an static analysis, equal to the displacement/stresses of an FE transient analysis?