The effects of material uncertainty on low-to high frequency vibrations of thin plates using a statistical moment based approach

The study presents an investigation for the effects of material uncertainty for low-to-high frequency vibration analyses of thin plates utilizing a statistical moment-based probabilistic approach. The uncertainty in the material properties is simulated by means of variabilities on structural damping, thickness, material density and elasticity. These variabilities are randomly modelled with shifted mean normal distributions. The approach carries out statistical moments of natural frequencies and vibration displacements of the plate by solving stochastic partial differential equation of bending vibration of the plate. The differential equation is handled by using discrete singular convolution method. Statistical moments of natural frequencies and vibration responses are estimated for several uncertainty sets generated by combination of four different material parameters; structural damping, thickness, density and elasticity. All predictions including combined effects of random parameters are compared with those of Monte Carlo simulations. Proposed approach clearly shows its considerable accuracy even in high modal overlapping regions with very efficient computation memory and time compared to Monte Carlo simulations. (paper)