random vibration fatigue - normal mode method

[rybose]

All of the literature available I've found on random vibration fatigue assumes the existence of a stress response PSD. This is required for the many methods that estimate fatigue life of broadband vibration response (i.e. Dirlik).

The FEA package I use, applies the Normal Mode Method to approximate the response of a structure to random vibration. In other words, the RMS response of the structure at each mode is calculated. So, instead of an output PSD, there is a sort of ‘discrete frequency response’ with an RMS stress value for each modal frequency. For example:

fn (Hz) RMS sigma_VM (ksi)
------- ----------------------
10 3
25 9
50 2
150 1

Given this information how do I ...

- Convert this to a PSD?
--> For example, one way might be to assume some constant bandwidth (del_f) to set the stess PSD value to RMS^2/(del_f). This would make the stress response PSD look like a series of bars of constant bandwidth.

OR

- Apply Miner’s rule directly to estimate fatigue life?


Thanks,
Ryan

 

[rybose]

Well, it seems to me that of the few people with random vibration experience, they all use FEA software packages that use the 'Direct Method' to solve for the response in terms of a PSD.

I use ALGOR which uses the 'Normal Mode Method' which approximates the response as the sum of modal responses.

I came up with a time domain approximation method that avoids converting the discrete response data to a PSD. The time domain of the response is modeled as the sum of sine functions with one sinusoid for each natural frequency.

X(t) = sum{ A_k * sin(w_k*t) }
k = 1 to n where n is the # of modes
w_k is the natural frequnecy at the kth mode
A_k is the amplitude of the response.
The amplitude A_k of each mode is randomly varied throughout time according to the Rayleigh distribution.

After X(t) is simulated, the fatigue life can be calculated using rainflow cycle counting methods. This method is exact for the narrowband case (1 modal response) and matches up well with sharply bi-modal PSDs.