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<p>This work investigates the thermoelastic free vibration behavior of functionally graded porous (FGP) sandwich plates with bi-directional thickness variations using the finite element method (FEM) under various boundary conditions. The sandwich configuration comprises a porous ceramic core and two porous sigmoid functionally graded facesheets. The kinematic relations and thermoelastic constitutive equations are formulated within higher-order shear deformation theory (HSDT), and Lagrange’s equation is used to derive the governing equations, including geometric stiffness to capture thermal nonlinearity. The study presents the natural frequencies of FGP sandwich tapered plates considering the combined effects of sandwich scheme, material gradation, porosity distribution, taper ratio, boundary conditions, and temperature rise. Results show that under cantilever conditions, the fundamental frequency decreases with increasing spanwise taper and increases with chordwise taper, while for simply supported and clamped plates, frequencies increase with both taper types across all sandwich configurations. The novelty of this work lies in formulating a free vibration model for porous sigmoid functionally graded material (S-FGM) sandwich tapered plates with a porous ceramic core under arbitrary boundary conditions operating in thermal environments. The scientific contribution is the reliable prediction of thermally influenced vibration characteristics, offering guidance for designing lightweight, high-temperature aerospace, energy, and automotive structures.</p>

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Free vibration analysis of porous sigmoid functionally graded sandwich tapered plates under arbitrary boundary conditions in thermal environment

  • 期刊论文

  • 发表日期：

    2026年3月16日

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  • Swagata Shannigrahi,
  • Tripuresh Deb Singha,
  • Tanmoy Bandyopadhyay

摘要

This work investigates the thermoelastic free vibration behavior of functionally graded porous (FGP) sandwich plates with bi-directional thickness variations using the finite element method (FEM) under various boundary conditions. The sandwich configuration comprises a porous ceramic core and two porous sigmoid functionally graded facesheets. The kinematic relations and thermoelastic constitutive equations are formulated within higher-order shear deformation theory (HSDT), and Lagrange’s equation is used to derive the governing equations, including geometric stiffness to capture thermal nonlinearity. The study presents the natural frequencies of FGP sandwich tapered plates considering the combined effects of sandwich scheme, material gradation, porosity distribution, taper ratio, boundary conditions, and temperature rise. Results show that under cantilever conditions, the fundamental frequency decreases with increasing spanwise taper and increases with chordwise taper, while for simply supported and clamped plates, frequencies increase with both taper types across all sandwich configurations. The novelty of this work lies in formulating a free vibration model for porous sigmoid functionally graded material (S-FGM) sandwich tapered plates with a porous ceramic core under arbitrary boundary conditions operating in thermal environments. The scientific contribution is the reliable prediction of thermally influenced vibration characteristics, offering guidance for designing lightweight, high-temperature aerospace, energy, and automotive structures.