Abstract
This chapter is dedicated to studying the influence of material uncertainties on the vibration characteristics of a functionally graded (FG) beam. Here, the uncertainties are assumed to be associated with Young’s modulus and material density of the metal constituent in special fuzzy numbers, namely Triangular Fuzzy Number (TFN). The governing equations for the vibration of the uncertain model are obtained by incorporating the Euler–Bernoulli beam theory along with a double parametric form of fuzzy numbers. Hermite–Ritz method is employed to calculate the results for Hinged–Hinged (HH) and Clamped–Clamped (CC) boundary conditions of the uncertain models for the lower bound and upper bound of the natural frequencies. The results obtained by the uncertain model are validated with the deterministic model exhibiting robust agreement. Further, a parametric study is conducted to investigate the fuzziness or spreads of the natural frequency concerning different uncertain parameters.