The dependence of the jump in the critical follower force for a viscoelastic bar on the form of the non-linear internal viscosity

The transverse oscillations of a viscoelastic bar under the action of a follower force are considered. The constitutive relation is the non-linear relation between the stress, strain and strain rate, where the non-linear part is described by a homogeneous form of the fifth degree. A numerical-analytical investigation of the stability showed that the three values of the critical follower force, corresponding to each of the three coefficients of viscosity available in the model, are independent of these coefficients and change in comparison with the case of a cubic viscosity.