  We consider a segmented structure, possibly connected with a continuous
medium, as initially homogeneous, where discontinuities arise as localized
strains induced by self-equilibrated localized actions. Under this formulation
augmented by interface conditions, the linearized formulation remains valid.
This approach eliminates the need for examining separate sections with
subsequent conjugation. Only conditions related to the discontinuities should
be satisfied, while the continuity in other respects preserves itself
automatically. No obstacle remains for the continuous Fourier transform. For a
uniform partitioning, the discrete transform is used together with the
continuous one. We demonstrate the technique by obtaining the Floquet wave
dispersive relations with their dependence upon interface stiffness. To this
end, we briefly consider the flexural wave in the segmented beam on Winkler's
foundation, the gravity wave in a plate (also segmented) on deep water and the
Floquet-Rayleigh wave in such a plate on an elastic half-space. Besides, we
present the wave equations developed for an elastic medium with
discontinuities.
