Localized vibrational modes in a quasi-one-dimensional lattice with a macrodefect

The vibrational spectrum of a quasi-one-dimensional lattice with a crack-like macrodefect is studied. The localized vibrational modes of two types are found to exist in a system: (i) low-frequency vibrational modes localized inside the defect; (ii) high-frequency vibrational modes localized outside the defect. The elastic relaxation length is estimated for localized modes of both types.