Investigation into the effect of random material properties on the variability of natural frequency of functionally graded beam

Abstract

In this study, the stochastic finite element solution is given to obtain the response variability in the natural frequency of Functionally Graded Material (FGM) beam due to uncertain structural parameters. Among others, the elastic modulus and mass density are chosen to have randomness along the beam axis direction, which are modeled as one-dimensional homogeneous stochastic processes. The stochastic analysis of the FGM beam is performed in conjunction with Monte Carlo simulation (MCS). Random samples of random parameters are generated based on the spectral representation method. The response variability in the natural frequency of FGM beam, due not only to the single random parameter of elastic modulus or mass density but also to both of the random parameters taken into account at the same time is investigated. The effect of respective random parameters on the response variability of natural frequency and the effect of correlation between the two random parameters as well are discussed in detail.

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