Dynamic stability of the rotating shaft made of Boltzmann viscoelastic solid.

*(English)*Zbl 0588.73090A general theory is developed in this paper for studying the dynamic stability of high-speed nonuniform rotating shafts made of a Boltzmann viscoelastic solid. The equation of motion of the shaft is deduced. The stability criteria are derived by using this equation. The unstable regions for a nonhomogeneous viscoelastic shaft are worked out numerically. Analytical formulas are also given in this paper for determining the planar deflection of the shaft and its inclined angle due to a planar static load. The conclusions for special cases given in the literature known to the authors are all covered by the results in this paper.

##### MSC:

74H55 | Stability of dynamical problems in solid mechanics |

74E05 | Inhomogeneity in solid mechanics |

74D99 | Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials) |

74D05 | Linear constitutive equations for materials with memory |

74D10 | Nonlinear constitutive equations for materials with memory |