THEORETICAL AND APPLIED MECHANICS

TEORIJSKA I PRIMENJENA MEHANIKA  2003 Vol.30 (3), pp.193-208

Summary: 

R. Ratko Pavlović, Predrag Kozić

Almost sure stability of the thin-walled beam
subjected to end moments

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, dumping coefficient, geometric and phisical parameters of the beam. The stability regions for I-cross section and narrow rectangular cross section are shown in variance - dumping coefficient plane when stochastic part of moment is Gaussian zero-mean process with variance s² and harmonic process with amplitude A.