Stochastic free vibration analysis of FG-CNTRC plates based on a new stochastic computational scheme

Abstract

Stochastic analysis can provide more accurate results compared to deterministic analysis. In this study, the spatial variability of material parameters is introduced into the free vibration analysis of functionally graded carbon nanotube reinforced composite (FG-CNTRC) plates to achieve a higher degree of accuracy, and a new stochastic computational scheme is proposed to handle the low-level uncertainties. First-order shear deformation theory (FSDT) is employed to establish the displacement field of the plates. The Young's moduli of carbon nanotube (CNT) and matrix are regarded as one-dimensional (1D) and two-dimensional (2D) random fields, respectively, which is discretized by Karhunen-Loève (K-L) expansion. The obtained random variables are substituted into modified perturbation stochastic method (MPSM) and radial point interpolation method (RPIM) to calculate the first two order estimates of the stochastic non-dimensional natural frequencies ω¯. The sensitivity of the first to fourth ω¯ to the random fields is analyzed, and the corresponding stochastic bands are plotted. The results indicate that the presented approach can accurately solve the generalized eigenvalue problem in stochastic free vibration; ω¯ is sensitive to random fields E11CNT and Em, and insensitive to random field E22CNT; the CNT distribution mode also affects the sensitivity.