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Dynamic stability of the rotating shaft made of Boltzmann viscoelastic solid. (English) Zbl 0588.73090
A 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.

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
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