Ergo this method becomes appropriate at certain cut-off frequencies. Do you agree with that
I'll give my simplistic thoughts fwiw (which probably duplicates what others have said and might miss some important).
There is a cutoff frequency which you could deduce from the speed of sound in a "structure" (*)
If the structure is a pure homogeneous material, then you could calculate speed of sound from material properties).
We remember the relationship among wavelength, frequency and speed of sound in the structure as follows:
wavelength = speed-of-sound / frequency
To predict behavior without considering waves, we need to have a wavelength much longer than the structure:
wavelength >> structure longest dimension.
subsitute our expression for wavelength:
speed-of-sound / frequency >> structure longest dimension.
Rearrange:
frequency << speed of sound / structure longest dimension
If frequency is low enough to satisfy this requirement (or equivalently structure small enough to satisfy this requirement), the structure can be analysed without considering wave behavior.
* Now the question: what is the "structure" of interest. I think it is the element size selected for the FEA. I think that is what hacksaw was getting at... you can analyse higher frequencies with your model if you refine to decrease the mesh size.
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(2B)+(2B)' ?