On the instability of the free elastic rod with non-linear intrinsic viscosity under the action of the follower force

A homogeneous free viscoelastic rod with constant cross-section is under the action of the follower force which has constant value is considered. It is well-known that for elastic rod the critical value of the follower force is approximately equal to p=109,7 (dimension free value). The main result consists of stability loss at presence of non-linear viscosity. The critical value of the follower force is p=83,1.