The Problem on Normal Oscillations of a System of Bodies Partially Filled with Viscous Fluids under the Action of Elastic-Damping Forces

In this paper, we study the problem on normal oscillations of a system of bodies partially filled with viscous fluids under the action of elastic and damping forces. It is proven that the nonzero spectrum of the problem is discrete and condenses towards zero and infinity. Asymptotic formulae for the eigenvalues are proved. A theorem on the \(p\) -basicity of the system of root elements of the problem is proven.