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<p>This study presents a comprehensive investigation into the vibrational behavior of functionally graded graphene nanoplatelet-reinforced composite (FG-GPLRC) plates interfacing with elastic substrates of variable stiffness. Utilizing a Winkler–Pasternak model, we examine how discrete substrate stiffness zones influence dynamic responses. Temperature-dependent material properties are rigorously characterized using a combined Halpin–Tsai micromechanical model and the rule of mixtures, capturing the nuanced effects of thermal environments. The governing equations, derived from Reddy’s third-order shear deformation theory and incorporating von Kármán geometric nonlinearity, are solved using the Galerkin method. The accuracy of the proposed approach is rigorously validated through comparisons with finite element method (FEM) simulations and benchmark results from the existing literature. This study explores key phenomena, including natural frequencies, central deflection time histories, resonance, and harmonic beat effects, while systematically assessing the impacts of thermal conditions, graphene reinforcement, applied voltage, and geometric parameters. Notably, an in-depth analysis of substrate stiffness variations leads to the formulation of a novel constraint equation for elastic substrates with equivalent stiffness. These findings not only enhance the theoretical framework of FG-GPLRC plates but also provide valuable insights for advancing structural design and engineering applications.</p>

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Nonlinear dynamics of nanocomposite plates supported by abruptly varied stiffness elastic substrates under electro-thermo-mechanical loadings

  • 期刊论文

  • 发表日期：

    2025年8月11日

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  • Vu Ngoc Viet Hoang,
  • Pham Trung Thanh

摘要

This study presents a comprehensive investigation into the vibrational behavior of functionally graded graphene nanoplatelet-reinforced composite (FG-GPLRC) plates interfacing with elastic substrates of variable stiffness. Utilizing a Winkler–Pasternak model, we examine how discrete substrate stiffness zones influence dynamic responses. Temperature-dependent material properties are rigorously characterized using a combined Halpin–Tsai micromechanical model and the rule of mixtures, capturing the nuanced effects of thermal environments. The governing equations, derived from Reddy’s third-order shear deformation theory and incorporating von Kármán geometric nonlinearity, are solved using the Galerkin method. The accuracy of the proposed approach is rigorously validated through comparisons with finite element method (FEM) simulations and benchmark results from the existing literature. This study explores key phenomena, including natural frequencies, central deflection time histories, resonance, and harmonic beat effects, while systematically assessing the impacts of thermal conditions, graphene reinforcement, applied voltage, and geometric parameters. Notably, an in-depth analysis of substrate stiffness variations leads to the formulation of a novel constraint equation for elastic substrates with equivalent stiffness. These findings not only enhance the theoretical framework of FG-GPLRC plates but also provide valuable insights for advancing structural design and engineering applications.