Geodesic
Influence of rotatory inertia on stochastic stability of a viscoelastic rotating shaft
Theoretical and applied mechanics, Tome 35 (2008) no. 4, p. 363 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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 $\sigma^2$ as well as for harmonic process with amplitude H.
DOI : 10.2298/TAM0804363P
Classification : 93E15 74D05
Keywords: Random loading, Liapunov functional, Almost sure stability, Rotatory inertia, Gaussian and harmonic process 
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     author = {Ratko Pavlovi\'c and P. Kozi\'c and G. Janevski},
     title = {Influence of rotatory inertia on stochastic stability of a viscoelastic rotating shaft},
     journal = {Theoretical and applied mechanics},
     pages = {363 },
     year = {2008},
     volume = {35},
     number = {4},
     doi = {10.2298/TAM0804363P},
     zbl = {1224.93126},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/TAM0804363P/}
}
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Ratko Pavlović; P. Kozić; G. Janevski. Influence of rotatory inertia on stochastic stability of a viscoelastic rotating shaft. Theoretical and applied mechanics, Tome 35 (2008) no. 4, p. 363 . doi: 10.2298/TAM0804363P

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