Going back through some (elastic) wave propagation texts of mine, this appears to be a necessary boundary condition when using the wave types necessary in periodic structures (i.e. structures composed of repetitive similar units) or composite type structures.
Of course, the boundary conditions are critical in any wave propagation study.....but unless you are doing some unusual nondestructive testing for your field (your discipline is marked as "Civil/Environmental").....I'm not sure how much use it is.
Then again, for all I know, this boundary condition could be used in some spectral FEA software (somewhere) for other applications.