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<p>This paper introduces a vibration analysis of graphene platelets (GPL)-reinforced functionally graded material (FGM) nanoplates placed on a Pasternak elastic medium for the first time. Four GPL patterns (i.e., FG-X, FG-O, FG-V, and UD) in combination with power-law (P-), exponential (E-), and sigmoid (S-) FGMs are examined. By applying Hamilton’s principle and using Reddy’s plate theory (Reddy’s TSDT), surface elasticity theory (SET), and nonlocal strain gradient theory (NSGT), the governing equations of motion for the nanoplate model resting on the elastic substrate medium are established. The Navier solution is presented to determine the natural frequencies of the simply supported nanoplates. Numerical investigations are performed to evaluate the influences of the&#xa0;NSGT parameters, the&#xa0;SET, the&#xa0;material parameters, and the&#xa0;foundation coefficients on the natural frequency of the nanoplate. The findings show the significant influences of the surface energy and the GPL weight fraction on the fundamental frequency of the nanoplate. When performing calculations with different size-dependent theory models, the impact of increasing GPL content on the fundamental frequency is relatively consistent. The P-FGM nanoplate reinforced by the FG-X GPL pattern is significantly more efficient than the other GPL distribution patterns. The stiffer the elastic medium, the less effective the GPL reinforcement for the nanoplate becomes.</p>

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Free Vibration Analysis of Graphene-Reinforced FGM Nanoplates with Surface Energy Effects Resting on Elastic Foundation

  • 期刊论文

  • 发表日期：

    2025年2月10日

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  • Thanh-Binh Chu,
  • Van-Loi Nguyen,
  • Minh-Tu Tran,
  • Van-Long Nguyen,
  • Xuan-Trung Dang

摘要

This paper introduces a vibration analysis of graphene platelets (GPL)-reinforced functionally graded material (FGM) nanoplates placed on a Pasternak elastic medium for the first time. Four GPL patterns (i.e., FG-X, FG-O, FG-V, and UD) in combination with power-law (P-), exponential (E-), and sigmoid (S-) FGMs are examined. By applying Hamilton’s principle and using Reddy’s plate theory (Reddy’s TSDT), surface elasticity theory (SET), and nonlocal strain gradient theory (NSGT), the governing equations of motion for the nanoplate model resting on the elastic substrate medium are established. The Navier solution is presented to determine the natural frequencies of the simply supported nanoplates. Numerical investigations are performed to evaluate the influences of the NSGT parameters, the SET, the material parameters, and the foundation coefficients on the natural frequency of the nanoplate. The findings show the significant influences of the surface energy and the GPL weight fraction on the fundamental frequency of the nanoplate. When performing calculations with different size-dependent theory models, the impact of increasing GPL content on the fundamental frequency is relatively consistent. The P-FGM nanoplate reinforced by the FG-X GPL pattern is significantly more efficient than the other GPL distribution patterns. The stiffer the elastic medium, the less effective the GPL reinforcement for the nanoplate becomes.