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<p>This paper presents a comprehensive analytical investigation into the free vibration behavior of a novel lightweight sandwich plate subjected to hygrothermal environments. The structural assembly consists of a functionally graded porous core reinforced by graphene nanoplatelets (GPLs) and bounded by GPL-reinforced composite facesheets, resting on a three-parameter Kerr elastic foundation. A Quasi-3D Logarithmic Shear Deformation Theory (LSDT) is developed to accurately capture both shear and normal deformation effects without requiring shear correction factors. The governing differential equations are derived using Hamilton’s principle and solved analytically via Navier’s technique for simply supported boundary conditions. The validity of the proposed model is established through rigorous comparison with existing literature. A detailed parametric study reveals the significant influence of GPL mass fraction, dispersion patterns, and geometric aspect ratios on the vibrational response. Most notably, a counter-intuitive non-monotonic behavior is observed for symmetric porosity distributions, where natural frequencies unexpectedly recover at high void fractions (&gt; 50%) due to the dominant effect of mass reduction over stiffness degradation, offering a critical avenue for optimizing lightweight structural performance.</p>

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Analytical solution for hygro-thermo-elastic dynamic performance of Quasi-3D logarithmic shear-deformable lightweight plate positioned between GPL-reinforced skins

  • 期刊论文

  • 发表日期：

    2026年5月4日

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  • Weiwei Zhang,
  • Yanting Sun

摘要

This paper presents a comprehensive analytical investigation into the free vibration behavior of a novel lightweight sandwich plate subjected to hygrothermal environments. The structural assembly consists of a functionally graded porous core reinforced by graphene nanoplatelets (GPLs) and bounded by GPL-reinforced composite facesheets, resting on a three-parameter Kerr elastic foundation. A Quasi-3D Logarithmic Shear Deformation Theory (LSDT) is developed to accurately capture both shear and normal deformation effects without requiring shear correction factors. The governing differential equations are derived using Hamilton’s principle and solved analytically via Navier’s technique for simply supported boundary conditions. The validity of the proposed model is established through rigorous comparison with existing literature. A detailed parametric study reveals the significant influence of GPL mass fraction, dispersion patterns, and geometric aspect ratios on the vibrational response. Most notably, a counter-intuitive non-monotonic behavior is observed for symmetric porosity distributions, where natural frequencies unexpectedly recover at high void fractions (> 50%) due to the dominant effect of mass reduction over stiffness degradation, offering a critical avenue for optimizing lightweight structural performance.