*This guest contribution on the Altair Blog is written by the CAEfatigue Team, a member of the Altair Partner Alliance.*

Similar to the last blog post where we talked about frequency matching between the Solver FRF and the input PSD loading, there is also a need to have good frequency matching between the Solver FRF and a sine sweep input loading. Understanding this will ensure that you calculate accurate responses and, therefore, 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 two PSD’s and connecting transfer function as presented by the PSD Plotter in the CFV GUI (CFG).

However, we now want to apply a deterministic sine sweep to the analysis that will be included along with the random input PSD; many refer to this as “** sine on random**” input loading. Within CFV, this can be easily accomplished, but, we must be very careful to ensure the resolution of the sine sweep is sufficient to pick up the peaks in the Transfer Function. Otherwise, the sine sweep may miss the resonant frequencies and, therefore, not provide an accurate response PSD. This is no different than ensuring a good resolution / frequency match between the random input PSD and Transfer Function as discuss in our previous post.

**Frequency Resolution and Resonance Detection of the Sine Sweep**

What is a Sine Sweep?

Example of SINE on RANDOM Analysis.

Just to be very clear, a sine sweep applies a __single__ sine wave to a structure and after the responses are calculated, another sine wave is applied to the structure and then another; i.e. one after the other. This continues until all sine waves in the sweep have been applied and the responses from all sine waves have been added together. If a random PSD is also required, it is applied every time the single sine wave is applied, i.e. at the same time as the sine wave. Below is an example of a 9 Hz sine wave and a random PSD, which are applied together as a single EVENT in a SINE on RANDOM analysis within CFV. Note: CFV can also apply many sine waves at the same time (harmonic loading), if desired, but this would not be considered a sine sweep.

Let’s assume that the solver FRF analysis has been correctly executed and it captures the peak FRF responses that are in the structure. This will ensure the Transfer Functions (created within CFV) are accurate and contains all the response frequencies that accurately reflect the response of the model.

Consider the Transfer Function in the plot to the below. There is one significant peak in the Transfer Function where the worst-case stress is occurring. This peak is at **8.8 Hz**. We can use this information to define our sine sweep.

Within CFV, a sine wave sweep can be defined as a series of single sine waves using a **SINGSINE** entry, a **DETLOAD** entry or a **SINESW** entry. For this example, we will define a series of single sine waves using SINGSINE applied with a random, single input PSD loading (shown as the input PSD in the plot above). Note: CFV will allow a sine sweep __without__ the random PSD loading, if desired.

Our first sweep is a series of single sine waves between 2 Hz and 32 Hz with an amplitude of 1 G and a spacing of 2 Hz. This sweep is rather course in spacing and will miss the peak response at 8.8 Hz; i.e. nearest sine wave frequency in the sweep is 8 Hz.

Selecting the “worst case” element, we can see from the Event plot below, that the worst damage occurs at Event 108, which contains the 8 Hz sine wave with the random input PSD loading. The fatigue damage at this element for this frequency is 0.09. Total fatigue damage predicted from the application of all sine waves and random PSDs at this element is **0.12**, where a value of 1.0 would represent a fail. A User may mistakenly feel very comfortable with these results and assume the structure will not fail but the analysis had a course spacing in the sine sweep and the peak resonance was missed.

Our second sweep is a series of single sine waves between 2 Hz and 32 Hz with an amplitude of 1 G and a spacing of 1 Hz. In this sweep we have improved the frequency spacing but still fail to include the resonant frequency of 8.8 Hz; i.e. nearest sine wave frequency in the sweep is 9 Hz.

Selecting the same “worst case” element, we can see from the Event plot below, that the worst damage occurs at Event 1090, which contains the 9 Hz sine wave with the random input PSD loading. The fatigue damage at this element, for this frequency alone is 0.45. Total fatigue damage predicted from the application of all sine waves and random PSDs at this element is **0.69**, where 1.0 would represent a fail. A User may feel comfortable that this structure will pass because the damage is under 1.00 but what happens if we actually apply a sine wave at 8.8 Hz, which is the peak response frequency.

Our third, and final sweep is a series of single sine waves between 2 Hz and 32 Hz with an amplitude of 1 G and a spacing of 1 Hz (same as above). However, we will replace the 9 Hz sine wave with an 8.8 Hz sine wave to match the peak response frequency seen in the Transfer Function. Selecting the same “worst case” element, we can see from the Event plot below, that the worst damage occurs at event 1088, which contains the 8.8 Hz sine wave and the random input PSD loading. The fatigue damage at this element for this frequency alone is 0.80. Total fatigue damage predicted from the application of all sine waves and the random PSD at this element is **1.04**, where 1.0 would be a fail.

This result is significantly different from the first sweep that only predicted a total damage of 0.12 (due to a course sine wave spacing in the sweep) and the second sweep that predicted a total damage of 0.69 (better spacing but still missed the resonant frequency in the sweep).

**CONCLUSIONS:**

Under loading from a random PSD and a properly defined sine sweep (including the resonant frequency) the structure could fail from fatigue because the damage value is just above 1.0. This possibility of failure was missed when the sweep was inappropriately spaced or did not include the resonant frequency and the User could have thought, based on incomplete data, that the structure was acceptable.

Therefore, it is imperative to understand the resonant frequencies within your model, especially within the expected operational frequency range, and to include those frequencies within the sine sweep to get the best response prediction from your analysis.

Interested in learning more? visit CAEfatigue through the Altair Partner Alliance.