Accounting for elastic ties damping properties in generalised mathematical model of solids system mounted on elastic rod

When studying mechanical vibrations of various detail and mechanism members in many cases solid (or solid system) elastically mounted on elastic rod is a design scheme of researching. Previously authors proposed a generalized mathematical model in the form of hybrid differential equations system of given structure that describes dynamics of any systems of interrelated solids elastically mounted on elastic rod (Euler-Bernoulli beam). Analytical and numerical method of frequency equation construction has been drawn up in order to research natural oscillation of such a system. The article is devoted to further development of free oscillations researching analytical and numerical methods based on the generalized mathematical model of solids mounted on elastic rod taking into account damping properties of elastic ties.