Honeycomb structures have the geometry of the lattice network to allow the minimization of the amount of used material to reach minimal material cost and minimal weight. In this regard, this article deals with the frequency analysis of imperfect honeycomb core sandwich disk with multiscale hybrid nanocomposite (MHC) face sheets rested on an elastic foundation. The honeycomb core is made of aluminum due to its low weight and high stiffness. The rule of the mixture and modified Halpin–Tsai model are engaged to provide the effective material constant of the composite layers. By employing Hamilton’s principle, the governing equations of the structure are derived and solved with the aid of the generalized differential quadrature method (GDQM). Afterward, a parametric study is done to present the effects of the orientation of fibers ( $$\theta_{{\text{f}}} /\pi$$ ) in the epoxy matrix, Winkler–Pasternak constants ( $$K_{{\text{w}}}$$ and $$K_{{\text{p}}}$$ ), thickness to length ratio of the honeycomb network ( $$t_{{\text{h}}} /l_{{\text{h}}}$$ ), the weight fraction of CNTs, value fraction of carbon fibers, angle of honeycomb networks, and inner to outer radius ratio on the frequency of the sandwich disk. The results show that it is true that the roles of $$K_{{\text{w}}}$$ and $$K_{{\text{p}}}$$ are the same as an enhancement, but the impact of $$K_{{\text{w}}}$$ could be much more considerable than the effect of $$K_{{\text{p}}}$$ on the stability of the structure. Additionally, when the angle of the fibers is close to the horizon, the frequency of the system improves.

中文翻译：

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粘弹性多相增强全对称系统的频率模拟

蜂窝结构具有晶格网络的几何形状，可以最大限度地减少所用材料的数量，从而达到最低的材料成本和最低的重量。在这方面，本文讨论了具有弹性基础上的多尺度混合纳米复合材料 (MHC) 面板的不完美蜂窝芯夹层盘的频率分析。由于其重量轻且刚度高，蜂窝芯由铝制成。混合规则和修改后的 Halpin-Tsai 模型用于提供复合层的有效材料常数。运用哈密顿原理，借助广义微分求积法（GDQM）推导出结构的控制方程并求解。之后，进行了参数研究以呈现环氧树脂基体中纤维取向 ( $$\theta_{{\text{f}}} /\pi$$ ) 的影响，Winkler–Pasternak 常数 ( $$K_{{\ text{w}}}$$ 和 $$K_{{\text{p}}}$$ )，蜂窝网络的厚长比 ( $$t_{{\text{h}}} /l_{{ \text{h}}}$$ )、碳纳米管的重量分数、碳纤维的价值分数、蜂窝网络的角度以及夹心盘频率的内外半径比。结果表明，$$K_{{\text{w}}}$$ 和 $$K_{{\text{p}}}$$ 的作用确实与增强相同，但影响$$K_{{\text{w}}}$$ 对结构稳定性的影响可能比 $$K_{{\text{p}}}$$ 的影响要大得多。此外，当光纤的角度接近地平线时，系统的频率会提高。