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<p>This study develops a numerical model combining isogeometric analysis, third-order shear deformation theory (TSDT), and Gurtin-Murdoch (G-M) surface elasticity to investigate the free vibration of functionally graded porous (FGP) nanoplates with surface effects. A modified power-law model defines the effective material properties. After validating the model, parametric analyses examine how surface effects influence natural frequencies under varying gradient indices, porosity coefficients, geometric dimensions, and boundary conditions. Key findings include: (1) Natural frequencies increase with the porosity coefficient in non-uniformly porous FGP nanoplates, while uniform porosity exhibits gradient-index-dependent frequency variations that may increase, decrease, or show non-monotonic behavior depending on the material gradient. (2) The influence of surface effects on natural frequencies depends on the competition between surface stiffening and surface mass contributions, with frequency curve intersections observed at small gradient indices and low porosity coefficients for uniform distributions. (3) The relative surface stiffening effect strengthens with larger length-to-thickness ratios, but weakens with larger aspect ratios (being most pronounced for square plates), and diminishes with increasing plate thickness or stronger boundary constraints.</p>

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Free vibration isogeometric analysis of functionally graded porous nanoplates based on the TSDT incorporating surface effects

  • 期刊论文

  • 发表日期：

    2026年8月4日

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  • Ningxia Liu,
  • Wei Chen,
  • Peng Shi

摘要

This study develops a numerical model combining isogeometric analysis, third-order shear deformation theory (TSDT), and Gurtin-Murdoch (G-M) surface elasticity to investigate the free vibration of functionally graded porous (FGP) nanoplates with surface effects. A modified power-law model defines the effective material properties. After validating the model, parametric analyses examine how surface effects influence natural frequencies under varying gradient indices, porosity coefficients, geometric dimensions, and boundary conditions. Key findings include: (1) Natural frequencies increase with the porosity coefficient in non-uniformly porous FGP nanoplates, while uniform porosity exhibits gradient-index-dependent frequency variations that may increase, decrease, or show non-monotonic behavior depending on the material gradient. (2) The influence of surface effects on natural frequencies depends on the competition between surface stiffening and surface mass contributions, with frequency curve intersections observed at small gradient indices and low porosity coefficients for uniform distributions. (3) The relative surface stiffening effect strengthens with larger length-to-thickness ratios, but weakens with larger aspect ratios (being most pronounced for square plates), and diminishes with increasing plate thickness or stronger boundary constraints.