Geodesic
Almost sure stability of the thin-walled beam subjected to end moments
Theoretical and applied mechanics, Tome 30 (2003) no. 3.

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The dynamic stability problem of the thin-walled beams subjected to end moments is studied. Each moment consists of constant part and time-dependent stochastic non-white function. Closed form analytical solutions are obtained for simply supported boundary conditions. By using the direct Liapunov method almost sure asymptotic stability condition is obtained as function of stochastic process variance, damping coefficient, geometric and physical parameters of the beam. The stability regions for I-cross section and narrow rectangular cross section are shown in variance - damping coefficient plane when stochastic part of moment is Gaussian zero-mean process with variance σ2 and harmonic process with amplitude A.
Keywords: random loading, almost sure stability, Liapunov functional, Gaussian and harmonic processes, stability regions, mode number 
@article{TAM_2003_30_3_a2,
     author = {Ratko Pavlovi\'c and Predrag Kozi\'c},
     title = {Almost sure stability of the thin-walled beam subjected to end moments},
     journal = {Theoretical and applied mechanics},
     pages = {193 - 207},
     publisher = {mathdoc},
     volume = {30},
     number = {3},
     year = {2003},
     url = {http://geodesic.mathdoc.fr/item/TAM_2003_30_3_a2/}
}
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Ratko Pavlović; Predrag Kozić. Almost sure stability of the thin-walled beam subjected to end moments. Theoretical and applied mechanics, Tome 30 (2003) no. 3. http://geodesic.mathdoc.fr/item/TAM_2003_30_3_a2/