Air transportation constitutes a significant advancement in enhancing transportation efficiency. Nonetheless, when this modality is employed for the transit of large-scale armaments and equipment, the vibrational properties of these items within the aircraft’s cabin, coupled with potential deviations from their designated installation positions, emerge as critical factors that could compromise the safety of such transportation endeavors. To accommodate the unique environmental conditions of low-temperature and low-pressure prevalent in high-altitude air transportation, this model employs a fractal frequency formula for an expedited and accurate characterization of vibrational properties, while also providing a detailed analysis of the errors attributable to positional deviations in these vibration assessments. The findings of this research demonstrate that the computational accuracy achieved herein surpasses that of the variational iteration method (VIM) and the homotopy perturbation method (HPM). Moreover, the investigation into the damping effects of inertial forces within fractal dimensions unveils innovative prospects for optimizing nonlinear vibration systems under the challenging conditions of low-temperature and low-pressure environments.

航空运输在提高运输效率方面取得了重大进步。尽管如此，当采用这种方式运输大型武器和设备时，飞机机舱内这些物品的振动特性，加上与其指定安装位置的潜在偏差，成为可能危及此类武器和设备安全的关键因素。交通运输事业。为了适应高空航空运输中普遍存在的低温低压的独特环境条件，该模型采用分形频率公式来快速准确地表征振动特性，同时还详细分析了由以下因素引起的误差：这些振动评估中的位置偏差。这项研究的结果表明，本文实现的计算精度超过了变分迭代法（VIM）和同伦摄动法（HPM）。此外，对分形维数内惯性力阻尼效应的研究揭示了在低温低压环境的挑战性条件下优化非线性振动系统的创新前景。