Stochastic dynamic characteristics of FGM beams with random material properties

The random factor method is developed for the stochastic dynamic characteristics analysis of beams that are made of functionally graded materials (FGM) with random constituent material properties in this paper. The effective material properties of FGM beams are assumed to vary continuously through different directions according to the power law distribution. In the proposed method, the randomness of the dynamic characteristics is explicitly expressed by random factors of constituent material parameters, and the statistics (means and variances) of modal parameters can be analytically computed by the statistics of random inputs with little computational efforts. Compared with the first-order perturbation technique and the Monte-Carlo simulation method, the proposed method is illustrated and verified by a FGM cantilever beam with material variation through the thickness or axial direction, and the contributions of random material properties to the dispersion of dynamic characteristics for the structure are systematically investigated. The numerical results also show the dominant effect of constituent volume fraction index on the dispersion of dynamic characteristics.