Probabilistic analysis of effect of the porosities in functionally graded material nanoplate resting on Winkler-Pasternak elastic foundations

A free vibration of FGM nanoplate resting on Winkler-Pasternak elastic foundations is investigated based on two variable refined plate theory. The small scale effects are introduced using the nonlocal elasticity theory. The effect of material property, porosities, geometry and elastic foundation stiffnesses are presented, the present solutions are compared with those obtained by other researchers. The results are in a good agreement with those in the literature. The Monte Carlo method is used to predict the distribution function of the vibration response. According to the obtained results, we note that the porosities parameter are important factors influencing on the distribution function of ω¯. The uncertainty in the porosities parameter, have a significant effect on increasing the probability of failure of plate and reduced of durability of structure.