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This work presents the Monte Carlo simulation based on finite element analysis to investigate the natural frequencies of the beam on an elastic foundation with uncertain material. The elastic modulus is assumed as a homogeneous Gaussian random field. The random field is generated based on the spectral representation method. An iterative algorithm is employed using the finite element method to calculate natural frequencies with various the generated functions of elastic modulus. The effects of the random field on the response variability of natural frequencies and the effects of foundation coefficients are discussed in detail.

The free vibration of functionally graded material (FGM) beams on an elastic foundation and spring supports is investigated. Young\'s modulus, mass density and width of the beam are assumed to vary in thickness and axial directions respectively following the exponential law. The spring supports are also taken into account at both ends of the beam. An analytical formulation is suggested to obtain eigen solutions of the FGM beams. Numerical analyses, based on finite element method by using a beam finite element developed in this study, are performed in order to show the legitimacy of the analytical solutions. Some results for the natural frequencies of the FGM beams are given considering the effect of various structural parameters. It is also shown that the spring supports show the greatest effect on the natural frequencies of FGM beams.