Influence of rotatory inertia on stochastic stability of a viscoelastic rotating shaft

• Main Authors: Pavlović Ratko, Kozić P., Janevski G.
• Format: Article
• Language: English
• Published: Serbian Society of Mechanics & Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade 2008-01-01
• Series: Theoretical and Applied Mechanics
• Subjects: random loading; Liapunov functional; almost sure stability; rotatory inertia; Gaussian and harmonic process
• Online Access: http://www.doiserbia.nb.rs/img/doi/1450-5584/2008/1450-55840804363P.pdf

The stochastic stability problem of a viscoelastic Voigt-Kelvin balanced rotating shaft subjected to action of axial forces at the ends is studied. The shaft is of circular cross-section, it rotates at a constant rate about its longitudinal axis of symmetry. The effect of rotatory inertia of the shaft cross-section and external viscous damping are included into account. The force consists of a constant part and a time-dependent stochastic function. Closed form analytical solutions are obtained for simply supported boundary conditions. By using the direct Liapunov method almost sure asymptotic stability conditions are obtained as the function of stochastic process variance, external damping coefficient, retardation time, angular velocity, and geometric and physical parameters of the shaft. Numerical calculations are performed for the Gaussian process with a zero mean and variance σ2 as well as for harmonic process with amplitude H.