Frequency Domain Fatigue Analysis: The need for good resonance determination and frequency matching between the Solver FRF Analysis and the Input PSD

The following will explain the need for good frequency definition in both the Solver FRF analysis and the Input PSD so proper resonances are found for the Transfer Function and the frequency content is matched between the FRF analysis and the Input PSD.  Understanding these concepts will ensure that the intended conditions are defined to calculate accurate fatigue damage in the Frequency Domain using CAEfatigue VIBRATION (CFV).

Let’s use the example below:

In order to calculate fatigue damage and fatigue life in the frequency domain, we first need to generate the RESPONSE PSD that is the result of multiplying the TRANSFER FUNCTION by the INPUT PSD. The Transfer Function is calculated within CFV using the solver FRF stress data, and the Input PSD is defined directly within CFV. Below is an example of the three PSDs as shown by the PSD Plotter in the CFV GUI (CFG).

As can be seen in the plot, the shape and frequency content of the Response PSD is heavily dependent on the shape and frequency content of the Transfer Function.  If care is not taken in the Solver FRF calculation, it would be very possible to miss, for example, the peak amplitude (resonance) at 14 Hz in the Transfer Function and thus, it would completely change the shape and content of the Response PSD.  We will look at this more closely below.

Frequency Resolution for Resonance Detection

To the left are two Transfer Functions that were generated within CFV from two different Solver FRF analyses.  In one case, the peak amplitudes (resonances) near 40-45 Hz are recognized and accounted for by the User (blue, solid line) whereas, in the second case, the User failed to recognize the peak contribution and bypassed the 40-45 Hz frequency in the FRF analysis settings (orange, dashed line).

If we now use these Transfer Functions with a simple Input PSD, we can see the influence this mistake has on the shape and frequency content of the Response PSDs (see image to the right).

It is clear to see that the Response PSDs have different shapes and peak values.  Using the correct Transfer Function (blue, solid line), the frequency resolution in the FRF analysis has picked up the response peaks at 40-45 Hz and the correct amplitude values are passed through to the Response PSD.

However, in the second case (orange, dashed line), the Response PSD falsely shows that the max peak response is at 25 Hz and completely misses the significant resonances at 40-45 Hz.

This mistake by the User, will likely cause a significant difference in the fatigue damage and life calculations because the cumulative areas under both curves are very different, which significantly changes the Mvalue used by the Dirlik method (most common damage calculation method used in frequency domain fatigue calculations). Most solvers have parameters (like FREQ4 in Nastran), which guide the User in choosing correct frequency points around such resonances.

Frequency Matching

A keen observer may also have notice something else that is incorrect in our example above. Although the blue, solid line Transfer Function does accurately reflect the response of the model, the User failed to recognize that the points in the Transfer Function do not match up well with the points in the Input PSD, especially around 5 Hz, i.e. there is no Transfer Function frequency point at 5 Hz; nearest points are at 0.5 Hz and 25 Hz.

Within CFV, the Response PSD is generated by multiplying the value of the Transfer Function PSD point by the corresponding value of the Input PSD point.  When a Transfer Function point does not align with an Input PSD point, the nearest points are interpolated to generate a new value at the frequency from the Transfer Function (creates green dot on Input PSD).

However, the reverse does not happen; i.e. if a point on the Input PSD does not line up with a point on the Transfer Function, that Input PSD point is ignored in the Response PSD calculation (red arrow, empty red circle on Response PSD).

CFV does not change the Solver FRF stress results to add in or take away points to account for the Input PSD frequencies.  This could, in theory, be attempted for single input (real) PSD’s with corresponding real transfer functions but there would be difficult theoretical issues to resolve. However, it cannot be done for multi-input PSDs because of the difficulty to interpolate across complex cross PSD’s and the corresponding complex transfer functions. Hence, CFV requires the User to ensure the frequency resolution is sufficient in the FRF to match the Input PSD.

In this example, the Transfer Function does not have a defined point at 5 Hz so the contribution of the Input PSD at 5 Hz is ignored. Hence, this frequency mismatch produces an incorrect Response PSD at 5 Hz. Effectively, the Input PSD is changed based on the Transfer Function frequency points to create a modified Input PSD where the red dots line up with the Transfer Function points and the blue dots are ignored.

Therefore, to ensure the fatigue damage and life calculations are accurate, the User must consider frequency resolution (to detect resonances) and frequency match between the Solver FRF analysis and the Input PSD definition.  Below are the correct Input PSD, Transfer Function and Response PSD for this example, which reflect appropriate frequency content and matching.

Good frequency content and matching can be accomplished by a careful understanding of the expected resonances in the model and the expected input loading that will be applied as part of the fatigue analysis.  Once understood, an appropriate choice of solver parameters (such as “FREQ1” and “FREQ4” entries for Nastran) can be made to ensure the desired frequency resolution to pick up resonances and where the loading changes significantly in the Input PSD, i.e. for typical road load data, the Input PSD will likely require good Solver FRF frequency resolution in the 1.0 Hz to 10.0 Hz range.

This post is intended to provide an understanding of how frequency domain fatigue analysis is conducted in CFV.  Remember, providing accurate data in will ensure accurate results out.


*CAEfatigue Limited ( is a privately owned company with it’s world headquarters located in London, England.   CAEfatigue Limited is dedicate to developing random response and fatigue evaluation software for dynamic mechanical systems that is easy to use for the average Engineer or Designer.   The CAEfatigue Limited suite of products are in use across multiple industries throughout the world and have become the industry standard for use in the frequency domain. Share with:

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