Purpose <p>This study investigates the free vibration behavior of graphene platelet (GPL)–reinforced multidirectional (2D/3D) functionally graded (FG) nanocomposite plates. The objective is to examine how multidirectional material gradation and different GPL dispersion patterns influence the dynamic characteristics of such nanostructures.</p> Methods <p>The metal–ceramic matrix is graded simultaneously in two and three spatial directions using a multivariable power-law distribution, while GPLs are dispersed through the thickness following symmetric, asymmetric, and uniform patterns. The effective material properties of the graded matrix and GPL-reinforced composite are evaluated using the modified rule of mixtures and the Halpin–Tsai micromechanical model, respectively. A nine-variable higher-order shear deformation theory (HOSDT-9) is employed to formulate the governing equations through Hamilton’s principle, which are subsequently solved as a generalized eigenvalue problem to determine the natural frequencies.</p> Results <p>The results demonstrate that multidirectional material gradation and GPL dispersion patterns significantly affect the vibration characteristics of FG nanocomposite plates. Tailored graphene reinforcement notably enhances the structural stiffness and increases the natural frequencies of the plates. These findings provide valuable insights for the design and optimization of graphene-reinforced graded plate structures with improved dynamic performance.</p>

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Eigenfrequency Analysis of Graphene-Reinforced Functionally Graded Nanoplates with Multidirectional Material Gradation using Higher-Order Shear Deformation Theory

  • Shibabrata Mohapatra,
  • Kamal Kishore Joshi,
  • Nitin Sharma

摘要

Purpose

This study investigates the free vibration behavior of graphene platelet (GPL)–reinforced multidirectional (2D/3D) functionally graded (FG) nanocomposite plates. The objective is to examine how multidirectional material gradation and different GPL dispersion patterns influence the dynamic characteristics of such nanostructures.

Methods

The metal–ceramic matrix is graded simultaneously in two and three spatial directions using a multivariable power-law distribution, while GPLs are dispersed through the thickness following symmetric, asymmetric, and uniform patterns. The effective material properties of the graded matrix and GPL-reinforced composite are evaluated using the modified rule of mixtures and the Halpin–Tsai micromechanical model, respectively. A nine-variable higher-order shear deformation theory (HOSDT-9) is employed to formulate the governing equations through Hamilton’s principle, which are subsequently solved as a generalized eigenvalue problem to determine the natural frequencies.

Results

The results demonstrate that multidirectional material gradation and GPL dispersion patterns significantly affect the vibration characteristics of FG nanocomposite plates. Tailored graphene reinforcement notably enhances the structural stiffness and increases the natural frequencies of the plates. These findings provide valuable insights for the design and optimization of graphene-reinforced graded plate structures with improved dynamic performance.