Working with long duration transient events in a finite element world can be extremely computationally expensive. If those events are very long, like the wheel hub forces over the lifespan of a vehicle, then it is impossible to simulate. One technique to overcome this limitation is to use something called Random Loading, or Random Analysis.
If a time signal can be considered properly random then it can be transformed from the time to the frequency domain and is known as a Power Spectral Density plot, or PSD. A quick check of randomness is that any section of a time history transformed in this way should give the same outcome as the whole signal. These PSD’s are best thought of as a statistical representation of the amount of energy in the signal as a function of frequency.
These PSD’s are used in combination with a frequency response analysis. A unit excitation load is applied across the range of frequencies seen in the PSD and these responses are combined with the PSD to give an RMS response that represents one standard deviation of the response. Design decisions can then be made based on a certainty of survival, for example there is a 0.3% chance that the response will exceed 3 standard deviations or 3xRMS levels.
The benefit of this approach is that no matter the length of the time history, the PSD is only as ‘long’ as the frequency content within it, so analysis runtimes are controlled and realistic for design purposes.
This is all well and good for point loads like forces and accelerations, but what about pressure loads? Traditionally a uniform pressure is applied to a panel and excited across the frequency range and is combined with the PSD as already explained. This sort of loading is common in space launch payloads and defence industries. As you remember from your O level physics, as the frequency of the load varies so does the wavelength. If the size of the panel is small with respect to the wavelength then the uniform load approach is valid, but when the panel size is large there is the potential for the wavelength of the pressure wave to be smaller than the panel at higher frequencies so the pressure will vary across the panel potentially from positive to negative. The uniform assumption here doesn’t hold. So what can we do?
Actran Diffuse Field Acoustics simulation overcomes all of this by including the fluid domain within the analysis. We can apply a pressure PSD as a diffuse field and Actran takes care of transferring this to the structural mesh and calculating the RMS responses appropriately.
At DTE we have experience with this technology and have seen good correlation with physical test results.
If you would like to discuss this technology, or anything related to random loading, including fatigue with combined random and deterministic loads please get in touch.