Spectrum of One-dimensional Vibrations of a Layered Medium Consisting of a Kelvin–Voigt Material and a Viscous Incompressible Fluid

The paper considers a mathematical model for natural vibrations of a periodic layered medium. The medium consists of a viscoelastic Kelvin–Voigt material and a viscous incompressible fluid. For the given model, two homogenized models are derived. They correspond to the cases of transverse and longitudinal vibrations of the layered medium. It is shown that the spectrum of each homogenized model is the union of roots of the corresponding quadratic equations.