Spectrum of One-Dimensional Eigenoscillations of a Medium Consisting of Viscoelastic Material with Memory and Incompressible Viscous Fluid

We consider the initial-boundary value problem describing joint oscillations of periodically alternating layers viscoelastic material with memory and viscous incompressible fluid. Solving auxiliary problems on periodicity cell, we write corresponding homogenized show that eigenvalues boundary involved in spectra one-dimensional eigenoscillations original media are roots transcendental algebraic equations respectively. In case where perpendicular to layers, Hausdorff converge spectrum problem.