Influence of transverse shear on stochastic instability of symmetric cross-ply laminated plates

The dynamic instability problem of symmetrically laminated cross-ply plates, compressed by time-dependent stochastic membrane forces, is investigated. The effect of shear deformation is included in the formulation. By using the direct Liapunov method, bounds of the almost sure instability of cross-ply plates are obtained. Furthermore, it is shown how the viscous damping coefficient, variances of the stochastic forces, ratio of the principal lamina stiffnesses, number of layers, plate aspect ratio, and cross-ply ratio influence the instability regions. A special attention is given to the proper choice of two shear correction factors of the laminated plate. Numerical calculations are performed for the Gaussian process with a zero mean and variance σ² as well as for the harmonic process with an amplitude A.