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<p>Enriched formulations are efficient in linear analysis, but they are rarely applied to nonlinear vibrations due to the complexity of combining high-order enrichment functions with geometric nonlinearities. This paper bridges this gap by formulating an enriched beam element to study the nonlinear vibration of sandwich beams with a porous core and graphene platelet (GPL) reinforced face layers. The proposed element is based on Euler-Bernoulli theory and von Kármán nonlinearity, using higher-order hierarchical functions to enrich conventional interpolations. Nonlinear frequencies of the sandwich beams with various boundary conditions and sandwich configurations are predicted using a direct iterative method. Extensive parametric studies demonstrate that the proposed element is efficient, providing accurate nonlinear frequencies with substantially fewer elements and shorter computational times than the conventional model. Results reveal that the effect of porosity on nonlinear vibration is coupled with the GPL weight fraction, with the impact of porosity diminishing as GPL content increases. Furthermore, the beam with hinged-hinged ends is to be the most sensitive to variations in the GPL fraction and porosity coefficient, whereas the clamped-clamped beam is the least. The influence of GPL distribution patterns and sandwich configurations on the nonlinear vibration behavior is also examined and highlighted.</p>

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Enriched finite element modeling in nonlinear vibration of porous sandwich beams with GPL reinforcement

  • 期刊论文

  • 发表日期：

    2026年7月11日

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  • Cong Ich Le,
  • Ngoc Duyen Dang,
  • Thu Nga Dinh,
  • Dinh Kien Nguyen

摘要

Enriched formulations are efficient in linear analysis, but they are rarely applied to nonlinear vibrations due to the complexity of combining high-order enrichment functions with geometric nonlinearities. This paper bridges this gap by formulating an enriched beam element to study the nonlinear vibration of sandwich beams with a porous core and graphene platelet (GPL) reinforced face layers. The proposed element is based on Euler-Bernoulli theory and von Kármán nonlinearity, using higher-order hierarchical functions to enrich conventional interpolations. Nonlinear frequencies of the sandwich beams with various boundary conditions and sandwich configurations are predicted using a direct iterative method. Extensive parametric studies demonstrate that the proposed element is efficient, providing accurate nonlinear frequencies with substantially fewer elements and shorter computational times than the conventional model. Results reveal that the effect of porosity on nonlinear vibration is coupled with the GPL weight fraction, with the impact of porosity diminishing as GPL content increases. Furthermore, the beam with hinged-hinged ends is to be the most sensitive to variations in the GPL fraction and porosity coefficient, whereas the clamped-clamped beam is the least. The influence of GPL distribution patterns and sandwich configurations on the nonlinear vibration behavior is also examined and highlighted.