Dynamics of Mechanical Actions on Materials. Part 11. System with Two Irreversibly Deformable Bodies

Abstract

A rheological model and the dynamics of an open mechanical system are considered including the elastic element of a machine and a composite body consisting of two successively joined irreversibly deformable bodies with a single degree of freedom under the action of an external force. On loading the system below the elastic limit for both bodies the motion of the mechanical system is described by a second order classical dynamic system. Above the elastic limit for one of the bodies system movement is described by a third order dynamic system, and above the elastic limit for both bodies by a dynamic system consisting of two third order differential equations. The solution of this dynamic system has the nature of damping oscillation with an increase in damping factor as there is an increase in the ratio of elastic stiffnesses and strain hardenings to the viscous resistances of the deformable bodies.