Résumé
We introduce a model that generalizes the. Frenkel-Kontorova model and describes re one-dimensional (1D) composite system made of two subsystems which are treated on an equal footing. The gap structure of the phonon energy spectrum and the character of lattice vibration are studied. We show that the phason mode may be pinned or not depending on the form of the intersubsystem potential. For a weak intersubsystem interaction the structure of the phonon energy spectrum is universal and may be revealed by a gnomonic projection of Z(3) onto the plane. For a short-range harmonic interaction there ate similarities between this model of composite and 1D quasicrystals.