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<p>To account for manufacturing-induced spatial randomness, this study presents an effective random meshless method to examine the stochastic free vibration behavior of porous functionally graded material (FGM) cylindrical panels. The proposed framework utilizes the radial point interpolation method (RPIM) to reconstruct the displacement fields, employs the Karhunen-Loève expansion technique to discretize the spatially varying random fields, and integrates the modified perturbation stochastic method (MPSM) to efficiently evaluate the statistical quantities of structural responses. Targeting the complex spatial perturbations inherent in cylindrical shells, the calculation accuracy and applicability of four distinct higher-order shear deformation theories (HSDT) are systematically discussed. On this basis, the effects of seven spatially varying random field parameters, including panel thickness <i>h</i>, power-law exponent&#xa0;<i>χ</i>, porosity parameter&#xa0;<i>v</i>, Young’s modulus, and mass density of constituent ceramic and metallic materials, are systematically analyzed across five distinct porosity distribution patterns, supplemented by the construction of random response bands to evaluate the dispersion range of structural responses. Numerical findings indicate that stochastic variations in panel thickness and ceramic phase properties exert a dominant influence on the sensitivity of natural frequencies. While the effects of the power-law exponent <i>χ</i> and porosity parameter&#xa0;<i>v</i> fluctuate across distribution patterns, their stochastic sensitivity fluctuations remain minimal due to the shell’s mechanical filtering and volume‑averaging effects, with the Top Enhancement (TE) pattern exhibiting superior robustness against uncertainty. Finally, the different boundary conditions preserve an unchanged hierarchical sensitivity ranking of the random parameters, with minor variations in absolute values arising merely from boundary-stiffness coupling.</p>

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A Stochastic Method for High-Order Free Vibration Analysis of Porous FGM Cylindrical Panels Employing RPIM and Karhunen-Loève Expansion

  • 期刊论文

  • 发表日期：

    2026年7月25日

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  • Ping Xiang,
  • Zihe Wang,
  • Yufei Chen,
  • Denggao Chen,
  • Zhiyuan Zhou,
  • Zhanjun Shao

摘要

To account for manufacturing-induced spatial randomness, this study presents an effective random meshless method to examine the stochastic free vibration behavior of porous functionally graded material (FGM) cylindrical panels. The proposed framework utilizes the radial point interpolation method (RPIM) to reconstruct the displacement fields, employs the Karhunen-Loève expansion technique to discretize the spatially varying random fields, and integrates the modified perturbation stochastic method (MPSM) to efficiently evaluate the statistical quantities of structural responses. Targeting the complex spatial perturbations inherent in cylindrical shells, the calculation accuracy and applicability of four distinct higher-order shear deformation theories (HSDT) are systematically discussed. On this basis, the effects of seven spatially varying random field parameters, including panel thickness h, power-law exponent χ, porosity parameter v, Young’s modulus, and mass density of constituent ceramic and metallic materials, are systematically analyzed across five distinct porosity distribution patterns, supplemented by the construction of random response bands to evaluate the dispersion range of structural responses. Numerical findings indicate that stochastic variations in panel thickness and ceramic phase properties exert a dominant influence on the sensitivity of natural frequencies. While the effects of the power-law exponent χ and porosity parameter v fluctuate across distribution patterns, their stochastic sensitivity fluctuations remain minimal due to the shell’s mechanical filtering and volume‑averaging effects, with the Top Enhancement (TE) pattern exhibiting superior robustness against uncertainty. Finally, the different boundary conditions preserve an unchanged hierarchical sensitivity ranking of the random parameters, with minor variations in absolute values arising merely from boundary-stiffness coupling.