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<p>This paper investigates the free vibration behavior of functionally graded porous (FGP) nanoplates, simultaneously considering the effects of nonlocal strain gradient theory and surface energy using the Ritz method. Utilizing third-order shear deformation theory, the study accounts for nanoscale size effects and material property variations due to porosity. The theoretical model incorporates uniform and non-uniform porosity distributions, surface effects via Gurtin–Murdoch theory, and nonlocal strain gradient effects for accurate representation of mechanical behavior. The pb2-Ritz technique is employed to solve the governing equations under various boundary conditions. Validation examples are provided, followed by a parametric analysis exploring the influence of nonlocal and strain gradient parameters, porosity coefficient, aspect ratio, porosity distribution patterns, volume fraction index, boundary conditions, and foundation stiffness on vibration behavior. The findings emphasize the significance of nanoscale effects, offering valuable insights for the design and optimization of advanced nanoplate systems for applications in nano- and micro-electromechanical systems.</p>

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Simultaneous Consideration of Nonlocal Strain Gradient and Surface Effects in Free Vibration Analysis of Functionally Graded Porous Nanoplates by Ritz Method

  • 期刊论文

  • 发表日期：

    2026年3月14日

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  • Van-Long Nguyen,
  • Tien-Thinh Le,
  • Xuan-Trung Dang

摘要

This paper investigates the free vibration behavior of functionally graded porous (FGP) nanoplates, simultaneously considering the effects of nonlocal strain gradient theory and surface energy using the Ritz method. Utilizing third-order shear deformation theory, the study accounts for nanoscale size effects and material property variations due to porosity. The theoretical model incorporates uniform and non-uniform porosity distributions, surface effects via Gurtin–Murdoch theory, and nonlocal strain gradient effects for accurate representation of mechanical behavior. The pb2-Ritz technique is employed to solve the governing equations under various boundary conditions. Validation examples are provided, followed by a parametric analysis exploring the influence of nonlocal and strain gradient parameters, porosity coefficient, aspect ratio, porosity distribution patterns, volume fraction index, boundary conditions, and foundation stiffness on vibration behavior. The findings emphasize the significance of nanoscale effects, offering valuable insights for the design and optimization of advanced nanoplate systems for applications in nano- and micro-electromechanical systems.