Study of Stability of Free Viscoelastic Rod under Tracking Force

The stability of rectilinear shape of a free viscoelastic rod is studied. A tracking force with the constant value is applied at one of the rod ends. The Kelvin-Voigt model is considered. While comparing critical values of the tracking force under viscosity free condition with those obtained using the Kelvin-Voigt model the rectilinear shape of loss of stability has been revealed. A critical value of the tracking force is found and the behavior of real parts of roots of the characteristic equation depending on the tracking force value is investigated.