An effective approach for stochastic natural frequency analysis of circular beams with radially varying material inhomogeneities

The natural frequency of functionally graded material beams is closely related to the spatially varying material model. Specially when the model is stochastic due to the variability of observational data. In this regard, this paper presents an effective approach for stochastic natural frequency analysis of circular composite beams with radially varied material properties. The higher-order shear deformation based spectral element model is first setup for structural natural frequency analysis. The random field theory is introduced to represent the radially varied stochastic material properties. To improve numerical efficiency of the brute-force simulation method, a multivariate Gegenbauer polynomial based sparse regression model is proposed to mimic the structural uncertain natural frequency function. Several numerical examples are presented to examine the performance of this proposed approach. Results have illustrated the high efficiency and numerical accuracy of utilizing the sparse regression method for uncertain natural frequency analysis of composite beams with radially varied stochastic material properties.