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<p>Functionally graded (FG) graphene origami-enabled auxetic metamaterial (GOEAM) structures have gained significant attention in recent years owing to their exceptional mechanical properties. This paper presents an analysis of nonlinear vibration characteristics of FG-GOEAM beams, focusing on the influence of the coupling between damping and graphene origami (GOri) parameters. The effective material properties of the FG-GOEAM beams are determined using the genetic programming (GP)-assisted micromechanical model. The Kelvin-Voigt damping model is introduced, and the governing equations of the damped beam are derived using Timoshenko beam theory and von Kármán nonlinearity. Differential quadrature (DQ) method is employed to solve the nonlinear kinematic equations. A comprehensive parametric study is conducted to analyze the effects of GOri content, folding degree, temperature, and damping on the nonlinear vibration behavior of the FG-GOEAM beams. Numerical results demonstrate that damping alters the nonlinear vibration behavior of the FG-GOEAM beam by weakening the effects of GOri parameters. The dominant factor differs by FG distribution, with GOri content dominating in X-<i>W</i><sub>Gr</sub> distribution, whereas GOri folding degree dominates in U-<i>W</i><sub>Gr</sub> distribution. In X-<i>W</i><sub>Gr</sub> beams, increasing the damping coefficient reduces the enhancement of the nonlinear frequency caused by GOri content, with a maximum reduction of 7.81%. For U-<i>W</i><sub>Gr</sub> beams, damping weakens the frequency suppression associated with GOri folding degree, with the reduction declining to 4.57% at 100% folding degree. Additionally, when the bending and shear proportional constants are less than 2.5 × 10<sup>–5</sup> s, the maximum reduction in linear and nonlinear frequencies is approximately 2%, indicating that damping can be neglected under this condition.</p>

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Nonlinear damped vibrations of functionally graded graphene origami-enabled metamaterial beams with Kelvin-Voigt damping

  • 期刊论文

  • 发表日期：

    2025年12月3日

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  • Jinlong Yang,
  • Liangteng Guo,
  • Shaoyu Zhao,
  • Jie Yang

摘要

Functionally graded (FG) graphene origami-enabled auxetic metamaterial (GOEAM) structures have gained significant attention in recent years owing to their exceptional mechanical properties. This paper presents an analysis of nonlinear vibration characteristics of FG-GOEAM beams, focusing on the influence of the coupling between damping and graphene origami (GOri) parameters. The effective material properties of the FG-GOEAM beams are determined using the genetic programming (GP)-assisted micromechanical model. The Kelvin-Voigt damping model is introduced, and the governing equations of the damped beam are derived using Timoshenko beam theory and von Kármán nonlinearity. Differential quadrature (DQ) method is employed to solve the nonlinear kinematic equations. A comprehensive parametric study is conducted to analyze the effects of GOri content, folding degree, temperature, and damping on the nonlinear vibration behavior of the FG-GOEAM beams. Numerical results demonstrate that damping alters the nonlinear vibration behavior of the FG-GOEAM beam by weakening the effects of GOri parameters. The dominant factor differs by FG distribution, with GOri content dominating in X-WGr distribution, whereas GOri folding degree dominates in U-WGr distribution. In X-WGr beams, increasing the damping coefficient reduces the enhancement of the nonlinear frequency caused by GOri content, with a maximum reduction of 7.81%. For U-WGr beams, damping weakens the frequency suppression associated with GOri folding degree, with the reduction declining to 4.57% at 100% folding degree. Additionally, when the bending and shear proportional constants are less than 2.5 × 10–5 s, the maximum reduction in linear and nonlinear frequencies is approximately 2%, indicating that damping can be neglected under this condition.