Spectrum of one-dimensional eigenoscillations of two-phase layered composites

The spectrum of one-dimensional eigenoscillations of two-phase composites with a periodic structure is studied. Their phases are isotropic elastic or viscoelastic materials, and the period consists of $2M$ alternating plane layers of the first and second phases. Equations whose roots form the spectrum are derived and their asymptotic behaviour is investigated. In particular, it is established that all finite limits of sequences of the spectrum points depend on the volume fractions of the phases and do not depend on the number $M$ and distances between the layers boundaries inside the period.