Dynamic stability of a thin-walled beam subjected to axial loads and end moments

The dynamic stability problem of thin-walled beams subjected to combined action of axial loads and end moments is studied. Each force and moment 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 and uniform stochastic stability conditions are obtained as the function of stochastic process variance, damping coefficient, and geometric and physical parameters of the beam. The almost sure stability regions for I-cross section and narrow rectangular cross section are shown in the plane of variances of stochastic parts axial force and end moment. Uniform stochastic stability regions are shown in intensity of stochastic loadings and constant parts of axial loads and end moments.