Influence of Transverse Shear on Stochastic Instability of the Elastic Beam

In the case when Kirchhoff–Love hypotheses do not give satisfactory results, we have to take the rotatory inertia and transverse shear into account. This paper studies the elastic beam subjected to stochastic axial load, when transverse shear is taken into account. By using the direct Liapunov method, the bounds of the almost sure instability of beams as the function of the damping coefficient, variance of the stochastic force, geometric parameters, mode number, section shape factor and intensity of the deterministic component of axial loading, are obtained. Calculations are performed for the Gaussian process with zero mean and variance ², as well as for the harmonic process with amplitude A.