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<p>This study presents an advanced computational framework to analyze the free vibration and stability of bidirectionally functionally graded material (2D-FGM) beams. Unlike conventional models, the proposed formulation accounts for mechanical properties varying continuously along both longitudinal and thickness directions via a power-law distribution. A significant innovation of this work is the integration of a three-parameter viscoelastic foundation featuring a spatially variable Winkler modulus, Pasternak shear, and damping coefficients to capture realistic soil-structure interactions. Utilizing a Quasi-3D higher-order shear deformation theory, the model provides a rigorous representation of transverse shear and thickness stretching effects without requiring shear correction factors. Governing equations, derived via Hamilton’s principle, are solved to quantify the sensitivity of natural frequencies and critical buckling loads to complex material-substrate coupling. Numerical results highlight the combined effects of bidirectional gradation, spatially variable viscoelastic substrate properties, and boundary conditions on the natural frequencies and critical buckling loads. The developed formulation demonstrates high accuracy and robustness for modeling and analyzing the complex mechanical behavior of 2D-FGM beams resting on nonhomogeneous viscoelastic foundations, offering an effective tool for the design and optimization of advanced composite structural elements.</p>

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Quasi-3D modeling of 2D-FG beams on nonlinear viscoelastic foundations: dynamic response and stability

  • 期刊论文

  • 发表日期：

    2026年7月31日

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  • Riadh Bennai,
  • Hassen Ait Atmane,
  • Osman Bulut,
  • Mokhtar Nebab,
  • Siham Ait Yahia,
  • Ahmed Kehli

摘要

This study presents an advanced computational framework to analyze the free vibration and stability of bidirectionally functionally graded material (2D-FGM) beams. Unlike conventional models, the proposed formulation accounts for mechanical properties varying continuously along both longitudinal and thickness directions via a power-law distribution. A significant innovation of this work is the integration of a three-parameter viscoelastic foundation featuring a spatially variable Winkler modulus, Pasternak shear, and damping coefficients to capture realistic soil-structure interactions. Utilizing a Quasi-3D higher-order shear deformation theory, the model provides a rigorous representation of transverse shear and thickness stretching effects without requiring shear correction factors. Governing equations, derived via Hamilton’s principle, are solved to quantify the sensitivity of natural frequencies and critical buckling loads to complex material-substrate coupling. Numerical results highlight the combined effects of bidirectional gradation, spatially variable viscoelastic substrate properties, and boundary conditions on the natural frequencies and critical buckling loads. The developed formulation demonstrates high accuracy and robustness for modeling and analyzing the complex mechanical behavior of 2D-FGM beams resting on nonhomogeneous viscoelastic foundations, offering an effective tool for the design and optimization of advanced composite structural elements.