I am working on simulating train induced vibrations using finite element method. The minimum element size I am taking is L_s/12 (where Ls = Shear wave wavelength). I am simulating infinite boundary using perfectly matched layers. However I am not able to find a concrete answer as to what should be my minimum domain length over which to simulate? One of the books I am referring presents a convergence graph and states that it must be at-least 1 - 1.5*L_s (where Ls = Shear wave wavelength). The graph is presented from 0.5*L_S to 5*L_s and I see no difference at all (Please see figure attached). This is a bit confusing to me . Can somebody tell me or point me to a source where it is mentioned as to how to decide the domain size that needs to be simulated for a particular frequency.
Thanks
Hi
Unfortunately, I do not have a reference to give you. That said, most people working with soil reference this book. https://www.amazon.ca/Dynamic-Soil-Structure-Interaction-John-Wolf/dp/0132215659
However, there are some known rules of thumb to rely on. We know thar boundary conditions affect +/-1/6 of the wavelength at each end on structures. We know also that the acoustic source strength is affected when a countermeasure or countersource is positioned within 1/4 of the wavelength.
The above would constitute the absolute minimum distance from simulated object to boundary as your anechoic bounadry will not be 100% non-reflecting as there will be an impedance discontinutity as there is a difference between your layered soil model and the FE region.
Acoustics is simpler than soil as we there deal only with one wavetype bit, still, we can borrow some insights from there and use for the wave type with the longest wavelength.
Your boundary is in the nearfield (i.e. pressure and particle velocity is out of phase) when you keep 1/4 of a wavelength distance between your model and your boundary.
It usually works better if you have some distance between source and boundary. After all, your layered soil model assumes free wave propagation at its interface - it makes sense that the wave field at the boundray should as closely approximate such conditions, i.e. lie in the so called far field.
Anechoic chambers used for sound power measurements use, if memory serves me correctly, a least 5-6 wavelenghts. The distance source to microphone is stated to be 4 wavelengths or more in some sound power measurement standards that rely on far field conditions.
Looking at a simple acoustic monopole, far field (i.e. pressure and particle velocity withing 5 degrees of phase), is one wavelength.
So, all in all, I'd say a good model would need at least two wavelengths source edge to boundary distance, ideally more.
Hope this helps
Sincerely
Claes
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