A modified non-partial derivative perturbation meshfree approach with second-order statistical moments for vibration of cylindrical composite plate with random fields using KL expansion

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In this work, a non-partial derivative perturbation approach is developed with second-order statistical moments for vibration of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) cylindrical panels. To address uncertainties, the modified perturbation stochastic method (MPSM) is applied. The analysis is grounded in the first-order shear deformation shell theory (FSDT) and employs the shape functions of kernel particles from mesh-free methods to model the displacement field of the panels. The Young’s moduli of carbon nanotubes (CNTs) and the matrix are modeled as one-dimensional and two-dimensional random fields, respectively, and are discretized using the Karhunen-Loève (K-L) expansion. These random fields are mapped from rectangular to cylindrical regions to create a random field model for the cylindrical panels, and the first six eigenvalues and eigenfunctions are calculated. The MPSM and reproducing kernel particle method (RKPM) are then used to estimate the second-order moments of the structural random dimensionless natural frequencies. This method significantly reduces computational costs while maintaining high accuracy. The sensitivity of the natural frequencies to the random fields is also analyzed, considering the influence of multiple random variables, the panel’s aspect ratio, and the span angle, with stochastic bands plotted accordingly. The findings show that the natural frequencies are predominantly affected by the random fields E11CNT and Em, while the distribution of CNTs, the aspect ratio, and the span angle of the panel play a significant role in the sensitivity of the natural frequencies.