为了探究结构损伤对折叠石墨烯改性材料动力学行为的影响，本文利用有限元方法计算了石墨烯折纸（Graphene Origami, GOri）负泊松比功能梯度梁的裂纹尖端应力强度因子。结合旋转弹簧模型与一阶剪切变形理论，采用Ritz方法和Hamilton原理，推导了梁的自由振动方程，并求解了梁的固有频率。结果显示，由于呈梯度分布，石墨烯折纸的折叠度对裂纹尖端的应力强度因子的影响与裂纹长度相关。同时，当GOri靠近梁表面分布时，梁的基频增加。随着GOri质量分数的增加，梁的基频也增加。例如，当GOri的氢覆盖率为20%时，仅增加0.15%的GOri，梁的基频可提高达到3.9%。然而，随着GOri折叠度的增大，梁的基频却降低。进一步研究发现，改变GOri折叠度、分布梯度和浓度以提高梁的刚度，会同时导致梁的振动行为对裂纹更为敏感。

To explore the influence of structural damage on the dynamic behavior of folded graphene-modified materials, this study employed finite element methods to calculate the stress intensity factor at the crack tip of Graphene Origami (GOri) enabled gradient beams with a negative Poisson's ratio function. Combining the rotational spring model with the first-order shear deformation theory, the free vibration equation of the beam was derived using the Ritz method and Hamilton's principle, and the natural frequencies of the beam were solved. The results indicate that, due to its gradient distribution, the folded degree of graphene origami affects the stress intensity factor at the crack tip, which correlates with the crack length. Moreover, when GOris are distributed closer to the surface of the beam, the natural frequency of the beam increases. The natural frequency of the beam also increases with the increase of GOri mass fraction. For instance, with a hydrogen coverage rate of 20% for GOri, increasing GOri by only 0.15% can lead to a 3.9% increase in the natural frequency of the beam. However, as the folded degree of GOri increases, the natural frequency of the beam decreases. Further research reveals that changing the folded degree, distribution gradient, and concentration of GOri to enhance the stiffness of the beam also makes the beam more sensitive to the crack in its vibration behavior.