Abstract : This paper investigates the bending vibration behavior of functionally graded material (FGM) beams with inherent uncertainties in material and geometric properties. The study employs the Stochastic Wave Finite Element (SWFE) method to quantify the influence of these uncertainties on wave propagation and dispersive characteristics. The material gradation is described explicitly through the volume fraction distribution, and the effective properties are derived accordingly. Based on the Euler–Bernoulli beam theory, the elemental mass and stiffness matrices are formulated and integrated into the WFE framework to extract the dispersion curves and wavenumbers. Uncertainties are modeled as Gaussian random variables and propagated through Monte Carlo simulations to compute the mean and standard deviation of the wavenumber. The obtained stochastic dispersion results highlight the sensitivity of bending wave propagation to variations in FGM parameters. The findings demonstrate that the SWFE approach efficiently captures the probabilistic behavior of composite structures and provides a reliable basis for analyzing and designing uncertain FGM systems

Key words: Uncertainty, Wave finite element method, Functionally graded material, dispersion.