Although auxetic metamaterials exhibit unique and unusual mechanical properties, such as a negative Poisson's ratio, their mechanics remains poorly understood. In this study, we model a graded beam fabricated from graphene origami-enabled auxetic metamaterials and investigate its dynamics from the perspective of different shear deformation theories. The auxetic metamaterial beam is composed of multiple layers of graphene origami-enabled auxetic metamaterials, where the content of graphene origami varies through the layered thickness; both the auxetic property and other properties are varied in a graded manner, which are effectively be approximated via micromechanical models. The Euler-Bernoulli, third-order, and higher-order shear deformable refined beam theories are adopted to model the auxetic metamaterial beam as a continuous system. Following this, the governing motion equations are derived using the Hamiltonian principle and then are numerically solved using a weighted residual method. The obtained results provide a comprehensive understanding of how graphene origami content and its distribution pattern, graphene folding degree, and the utilisation of different shear deformation theories influence the dynamic behaviour of the beam.

中文翻译：

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通过各种剪切变形理论实现石墨烯折纸拉胀超材料梁的动力学


尽管拉胀超材料表现出独特且不寻常的机械性能，例如负泊松比，但对其力学仍然知之甚少。在这项研究中，我们对由石墨烯折纸拉胀超材料制成的梯度梁进行了建模，并从不同的剪切变形理论的角度研究了其动力学。拉胀超材料梁由多层石墨烯折纸拉胀超材料组成，其中石墨烯折纸的含量随着分层厚度的变化而变化；拉胀性能和其他性能均以分级方式变化，可通过微机械模型有效地近似。采用欧拉-伯努利、三阶和高阶剪切变形细化梁理论将拉胀超材料梁建模为连续系统。接下来，使用哈密顿原理导出控制运动方程，然后使用加权残差法进行数值求解。获得的结果提供了对石墨烯折纸含量及其分布模式、石墨烯折叠程度以及不同剪切变形理论的利用如何影响梁的动态行为的全面了解。