Abstract
We introduce a model that generalizes the Frenkel - Kontorova model and describes a 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 
onto the plane. For a short-range harmonic interaction there are similarities between this model of composite and 1D quasicrystals.