The Stochastic Finite Element in the Natural Frequency of Functionally Graded Material Beams

In this study, the stochastic finite element solution is given to obtain the variability in the natural frequency of functionally graded material (FGM) beam. The elastic modulus is assumed to vary in the thickness direction and the width of the beam to vary as well in the longitudinal direction following the exponential law. The random material properties of elastic modulus and mass density of the FGM beam are assumed to be one-dimensional homogeneous stochastic processes. The stochastic finite element analysis of FGM beam is performed in conjunction with Monte Carlo simulation (MCS) employing the spectral representation method for 16, the description of random processes of the random material properties under consideration. The response variability of the natural frequency due to random elastic modulus is evaluated for various states of randomness. Furthermore, the investigation on the effect of the correlation between random elastic modulus and random mass density on the response variability is addressed in detail as well.