Localised vibration modes and stop bands for continuous and discrete periodic structures

The paper analyses Bloch–Floquet waves propagating in doubly-periodic composite structures containing high-contrast interfaces and finite size defects. Dispersion diagrams are presented for waves in continuum elastic structures containing arrays of two-phase inclusions, as well as for discrete lattice structures with defects. Particular attention is paid to structures that filter waves of certain frequencies and possess highly localised vibration modes. The original concept is applied to analysis of the spectrum for structures accumulating damage.