Instability of non-linear viscoelastic beam under tracking loading

In this paper we study a stability of low oscillations of cantilever viscoelastic beam one end of that is rigidly fixed and another one is subjected to action of the constant by absolute value tracking loading. The beam material satisfies with the constitutive relation σ=Eε+k₁ε²ε˙+k₂ε˙³, where E is the Young module, k₁ and k₂ are the coefficients of non-linear viscosity. The critical loading by that the beam oscillations near the rectilinear state become unstable is obtained. The value of this loading differs from the analogous ones for elastic or linear viscoelastic by Voight materials. The Kamenkov´ criterion is used by numerical analysis.