MODEL OF QUASI-LINEAR RHEODYNAMIC MEDIUM AND ITS SOLUTION

Akmal A. Mirzoev, Ikhmat N. Khusanov

Abstract: This paper analyses the stable and unstable stress deformation states of elastic-viscous-inertial (retardation) model depending on the acting stress and rheological parameters of the medium. The introduced concepts: self-oscillatory deformation state, the soft mode of deformation, hard deformation mode, excitation coefficient of rheodynamcs system and others. For the initial conditions lying within the unstable, limit cycle the oscillatory deformation of rheodynamcs system is damping. For the initial conditions, located outside of this cycle, self-oscillatory deformation processes are set. Parameter ?, resulting in different values to the emergence and disappearance of self-oscillation in a medium, is called coefficient of stimulating rheodynamcs systems. However, an unlimited increase in the vibration strain requires unlimited admission of energy to the system. Therefore, in these cases, the approach taken under different ? is to be enough and take into account the higher-order terms.

Keywords: Deformable Medium, Linear Viscoelasticity, Viscous – Inert, A Rheodynamcs, A Quasi-Linear, SelfOscillatory, A Stable Equilibrium State

DOI: https://doi.org/10.15623/ijret.2016.0510006