Spectrum of one-dimensional natural vibrations of layered medium consisting of elastic material and viscous incompressible fluid

The spectrum of one-dimensional natural vibrations of a layered medium with a periodic structure consisting of an isotropic elastic material and a viscous incompressible fluid is studied. It is established that the spectrum points are the roots of transcendental equations. In order to solve these equations numerically for multi-layered media, the roots of quadratic equations are proposed to use as initial approximations.