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<p>This analytical study investigates the free vibration characteristics of functionally graded (FG) plates that contain manufacturing porosity. The authors employ a specialized secant hyperbolic higher-order shear deformation theory to accurately model transverse shear stresses without requiring shear correction factors. The plate materials are modeled using both power-law (P-FGM) and sigmoid-law (S-FGM) distributions for material variation, while considering five distinct porosity distribution models through the plate thickness. Applying Hamilton’s principle and Navier’s method to obtain analytical solutions for simply supported plates, the analysis quantifies the influence of key parameters such as the power-law exponent, porosity parameter, and aspect ratio. The investigation confirms the accuracy of the proposed formulation against existing data and concludes that the symmetric center-enhanced (SCE) porosity pattern consistently yields the highest fundamental frequency among the bottom-enhanced and top-enhanced distributions studied. Moreover, numerous numerical examples are presented to serve as benchmark references for future study on porous FG plates.</p>

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Vibration analysis of porous functionally graded plates in the framework of non-polynomial shear deformation theory: An Analytical Study

  • 期刊论文

  • 发表日期：

    2026年6月2日

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  • Mohit Dhuria,
  • Manu Dev Sharma,
  • Neeraj Grover,
  • Kavita Goyal,
  • Tinh Quoc Bui

摘要

This analytical study investigates the free vibration characteristics of functionally graded (FG) plates that contain manufacturing porosity. The authors employ a specialized secant hyperbolic higher-order shear deformation theory to accurately model transverse shear stresses without requiring shear correction factors. The plate materials are modeled using both power-law (P-FGM) and sigmoid-law (S-FGM) distributions for material variation, while considering five distinct porosity distribution models through the plate thickness. Applying Hamilton’s principle and Navier’s method to obtain analytical solutions for simply supported plates, the analysis quantifies the influence of key parameters such as the power-law exponent, porosity parameter, and aspect ratio. The investigation confirms the accuracy of the proposed formulation against existing data and concludes that the symmetric center-enhanced (SCE) porosity pattern consistently yields the highest fundamental frequency among the bottom-enhanced and top-enhanced distributions studied. Moreover, numerous numerical examples are presented to serve as benchmark references for future study on porous FG plates.