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<p>In this paper, we introduce a multi-directional isogeometric analysis (IGA) method to evaluate the natural frequency response for multi-directional functional gradient (MFG) plates, with a particular focus on the hygrothermal-free vibration behavior of circular/annular nano-functionally graded piezoelectric (NFGP) plates resting on a variable elastic foundation. An efficient nonuniform rational B-spline numerical method is developed using nonlocal strain gradient theory and first-order shear deformation theory (FSDT) to account for changes in porosity and variable elastic foundations. A series of numerical examples demonstrates the method’s accuracy and effectiveness, capturing key phenomena such as the&#xa0;consistent frequency reduction in annular plates compared to circular ones&#xa0;and the&#xa0;counterintuitive frequency increase under specific nonuniform hygrothermal loads. The influence of various parameters, including nonlocal parameters, porous size and distribution, temperature and humidity conditions, and variable elastic foundation, on the natural frequencies is systematically investigated. This study shows that the parabolic variable foundation yields superior frequency improvement compared to other variable foundations. Additionally, applied voltage and hygrothermal loading significantly influenced the vibration responses, and strong coupling is observed between parabolic variable foundations and hygrothermal conditions. This study establishes a comprehensive computational foundation for designing advanced nano-electromechanical systems (NEMS) and optimizing smart structures under multifield loading.</p>

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Multi-directional isogeometric analysis of hygrothermal vibration responses in circular/annular nano-functionally graded piezoelectric porous plates resting on variable foundations

  • 期刊论文

  • 发表日期：

    2026年4月16日

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  • Pawan Kumar,
  • Sontipee Aimmanee

摘要

In this paper, we introduce a multi-directional isogeometric analysis (IGA) method to evaluate the natural frequency response for multi-directional functional gradient (MFG) plates, with a particular focus on the hygrothermal-free vibration behavior of circular/annular nano-functionally graded piezoelectric (NFGP) plates resting on a variable elastic foundation. An efficient nonuniform rational B-spline numerical method is developed using nonlocal strain gradient theory and first-order shear deformation theory (FSDT) to account for changes in porosity and variable elastic foundations. A series of numerical examples demonstrates the method’s accuracy and effectiveness, capturing key phenomena such as the consistent frequency reduction in annular plates compared to circular ones and the counterintuitive frequency increase under specific nonuniform hygrothermal loads. The influence of various parameters, including nonlocal parameters, porous size and distribution, temperature and humidity conditions, and variable elastic foundation, on the natural frequencies is systematically investigated. This study shows that the parabolic variable foundation yields superior frequency improvement compared to other variable foundations. Additionally, applied voltage and hygrothermal loading significantly influenced the vibration responses, and strong coupling is observed between parabolic variable foundations and hygrothermal conditions. This study establishes a comprehensive computational foundation for designing advanced nano-electromechanical systems (NEMS) and optimizing smart structures under multifield loading.