<p>This paper presents a natural vibration analysis of functionally graded graphene origami-enabled auxetic metamaterial (FG-GOEAM) rotor blades, idealized as pre-twisted shallow conical shells. A finite element framework based on the first-order shear deformation theory (FSDT) is developed using an eight-noded isoparametric quadratic element. Various layerwise gradation schemes of graphene origami (GOri) content and folding degree across the thickness are considered to tailor the auxetic and stiffness characteristics of the composite blade. A genetic programming (GP)-assisted micromechanical model is employed to estimate the position- and temperature-dependent effective material properties. The dynamic equilibrium equations of the rotating blade operating at moderate rotational speeds under through-thickness thermal gradients are derived using Lagrange’s equations of motion. Two types of temperature gradients, namely linear and sinusoidal distributions, are considered. A comprehensive parametric study is carried out to investigate the effects of GOri content, GOri folding degree, length-to-reference width ratio, pre-twist angle, temperature gradient, and rotational speed on the natural frequencies. The numerical results demonstrate that the vibration characteristics can be effectively tuned through appropriate tailoring of the GOri reinforcement and its spatial distribution. The findings provide valuable design guidelines for the development of next-generation rotor blades with controllable dynamic behavior, thereby enhancing operational reliability and service life in turbomachinery, helicopter rotors, wind turbines, and other rotating systems operating under thermal gradients.</p>

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Functionally graded graphene origami-enabled auxetic metamaterial rotor blades with tunable natural vibration behavior under temperature gradients

  • Tripuresh Deb Singha,
  • Tanmoy Bandyopadhyay

摘要

This paper presents a natural vibration analysis of functionally graded graphene origami-enabled auxetic metamaterial (FG-GOEAM) rotor blades, idealized as pre-twisted shallow conical shells. A finite element framework based on the first-order shear deformation theory (FSDT) is developed using an eight-noded isoparametric quadratic element. Various layerwise gradation schemes of graphene origami (GOri) content and folding degree across the thickness are considered to tailor the auxetic and stiffness characteristics of the composite blade. A genetic programming (GP)-assisted micromechanical model is employed to estimate the position- and temperature-dependent effective material properties. The dynamic equilibrium equations of the rotating blade operating at moderate rotational speeds under through-thickness thermal gradients are derived using Lagrange’s equations of motion. Two types of temperature gradients, namely linear and sinusoidal distributions, are considered. A comprehensive parametric study is carried out to investigate the effects of GOri content, GOri folding degree, length-to-reference width ratio, pre-twist angle, temperature gradient, and rotational speed on the natural frequencies. The numerical results demonstrate that the vibration characteristics can be effectively tuned through appropriate tailoring of the GOri reinforcement and its spatial distribution. The findings provide valuable design guidelines for the development of next-generation rotor blades with controllable dynamic behavior, thereby enhancing operational reliability and service life in turbomachinery, helicopter rotors, wind turbines, and other rotating systems operating under thermal gradients.