On the spectrum of one-dimensional oscillations of a laminated composite with components of elastic and viscoelastic materials

We construct two averaged (effective) models corresponding to transverse and longitudinal oscillations of a laminated composite. The components of such a composite are mutually alternating layers of isotropic elastic and viscoelastic materials. We prove that the study of the spectrum of each of the averaged models is reduced to finding the roots of the corresponding linear fractional equations.